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Complex Berry phase and steady-state geometric amplification in non-Hermitian systems https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743988299406-9EJIVOU5V3ONFDB3C4IG/2.PNG Papers - Complex Berry phase and steady-state geometric amplification in non-Hermitian systems https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743988298846-X30MQW94CCZ67Y8RBWSV/3.PNG Papers - Complex Berry phase and steady-state geometric amplification in non-Hermitian systems https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743988297773-9WNAZX810O1OXB84YB5U/4.PNG Papers - Complex Berry phase and steady-state geometric amplification in non-Hermitian systems https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743988298049-L49FJFY7IQX98NXDRFLF/5.PNG Papers - Complex Berry phase and steady-state geometric amplification in non-Hermitian systems https://www.ysspatil.com/papers/resolving-the-topology-of-encircling-multiple-exceptional-points monthly 0.5 2025-04-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990731374-DKL82F0KKFUU6K6ORLBD/1.PNG Papers - Resolving the topology of encircling multiple exceptional points https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990731570-75MF12CDJTCTGYZAJO9B/2.PNG Papers - Resolving the topology of encircling multiple exceptional points https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990732432-UDP7GVW9GX9F22Q7NDTC/3.PNG Papers - Resolving the topology of encircling multiple exceptional points https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990732757-LWU3S1FITHNJS687NAOH/4.PNG Papers - Resolving the topology of encircling multiple exceptional points https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990733636-HVG6TYSSGNG4ZROUNKND/5.PNG Papers - Resolving the topology of encircling multiple exceptional points https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743990733798-DADJPJI73Z2AIIMI5WST/6.PNG Papers - Resolving the topology of encircling multiple exceptional points https://www.ysspatil.com/papers/a-proposal-for-detecting-the-spin-of-a-single-electron-in-superfluid-helium monthly 0.5 2025-04-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743996467128-BVZ3WX6QA39DLBGW7KMH/1.PNG Papers - A proposal for detecting the spin of a single electron in superfluid helium https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743996466208-T5ETXP1QJ7E6KH87CRTC/2.PNG Papers - A proposal for detecting the spin of a single electron in superfluid helium https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743996467213-WWP27KHPR4C2NB01HFUW/3.PNG Papers - A proposal for detecting the spin of a single electron in superfluid helium https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743996468046-GXOZ6LVYU7XUN01DSBAH/4.PNG Papers - A proposal for detecting the spin of a single electron in superfluid helium https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1743996468205-UB5VZ3YCA2K01DWJAZJX/5.PNG Papers - A proposal for detecting the spin of a single electron in superfluid helium https://www.ysspatil.com/papers/highordercoherences2021 monthly 0.5 2025-04-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580700113-H3GEPS6FM52MQ07Q9V9O/Fig1.png Papers - Measuring high-order phonon correlations in an optomechanical resonator (a) Device schematic: A fiber-based Fabry-Perot cavity is filled with superfluid $^4$He. Blue shading denotes the instantaneous $^4$He density in an acoustic mode. Orange denotes the optical mode intensity. (b) Optical schematic showing the two drive lasers (red and blue paths), optomechanical cavity (OMC, black dashed box), acoustically scattered photons (green path), two signal filter cavities (green) and the two SPDs. The filter cavities (red and blue) before the OMC are used to suppress laser phase noise. (c) Optical spectrum showing the frequencies of the lasers, scattered photons, and filters, all with respect to the OMC's optical resonance. (d) Photon count rate spectrum measured as a function of the drive laser detuning $\Delta$, with $P_\text{in} = 400$ nW. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580717440-T20NQ3LJ0TOI81RHSH5J/Fig2.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580747713-MPNUWE2CLITRKQVOTG54/Fig3.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580778883-3O6WEDVGBI12NVZFNQU1/Fig4.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580778890-HMA058NX6W4TJD5QDE6L/FigS1.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580963468-VVLZXM5KLNB0CGCKXQ9H/FigS2.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580962397-Q9SEHGEUP4MLE4RM7VF5/FigS3.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580779686-XP01F739ULIO9XD41PXQ/FigS4.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580779834-LTAVLRUJR3HEZLYP7POP/FigS5.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580780975-QNH17JXLP5WI4WYEVLG8/FigS6.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580781116-JBV77FXPSG195MUTTZJ9/FigS7.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580963225-AGGHKBS7FQ2IGOTA3QBF/FigS8.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580963744-02U80DTPF2ANM2PNDF0W/FigS9.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580963996-AQD4VEBK6DMPQ9GXCAE6/FigS10.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643580788396-6U0HTAV9XKU4PBXHUR92/FigS11.png Papers - Measuring high-order phonon correlations in an optomechanical resonator https://www.ysspatil.com/papers/knot2021 monthly 0.5 2023-02-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572507327-UL2P9KTPY4DHJYFQW5O7/Fig1.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572505468-0CQD9FXNWXXB9I6VTP3I/Fig2.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572507931-B6IAIGZCLBT7274RC5DY/Fig3.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572503822-UL89LU02UQJS2XONFDRQ/Fig4.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572503260-AXCP4ZJL53OBTAK2H5O3/Fig5.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572502656-N12R6ZHJWX1EDH0OMQVG/FigS1.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572500503-QUSODLRJIVE16QM06UF9/FigS2.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572500989-BJ2LS3HGBQBEZCRZ0V1F/FigS3.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572499889-XUKQ6I7XI8XVOLMSN9PW/FigS4.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572499317-6I8LG367ACAVC0CUC4CG/FigS5.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572497210-19BR3X44WHQSJ1342OXA/FigS6.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572499160-BVHQ1UPVJSP3VULRFWWM/FigS7.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572495528-5SGX5UIG7LA3FFEBBV87/FigS8.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572493801-M1PWRFULLX3L6XX38Y27/FigS9.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572495204-JP5QM2KWSO6V86IFSHTW/FigS10.png Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572492777-KZ8UW8RA39YO1SI8N7GK/FigS11.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1643572492254-QW94I8OZ8TNBFMAPW432/FigS12.jpg Papers - Measuring the knot of degeneracies and eigenvalue braids near a third-order exceptional point https://www.ysspatil.com/papers/system-design-of-a-cold-atom-gyroscope-based-on-interfering-matter-wave-solitons monthly 0.5 2025-04-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1744040822779-ANM7SZKRMRJ3ZBTFF83I/1.png Papers - System design of a cold atom gyroscope based on interfering matter-wave solitons https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1744040822770-KPBSEHA4V163B5FPANID/2.png Papers - System design of a cold atom gyroscope based on interfering matter-wave solitons https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1744040823429-VQBX8P0Y1P25Y5TMCAU7/3.png Papers - System design of a cold atom gyroscope based on interfering matter-wave solitons https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1744040823557-152Z3QKUSNPC3HYG434E/4.png Papers - System design of a cold atom gyroscope based on interfering matter-wave solitons https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1744040824259-QM6Z0BICJS8OK2FT1V8A/5.png Papers - System design of a cold atom gyroscope based on interfering matter-wave solitons https://www.ysspatil.com/papers/2017/9/23/coming-soon-critical-behavior-of-a-driven-dissipative-system-universality-beyond-the-markovian-regime monthly 0.5 2022-01-30 https://www.ysspatil.com/papers/2017/9/23/coming-soon-universal-critical-behavior-of-an-emergent-phase-with-a-spontaneously-broken-time-translation-symmetry monthly 0.5 2022-01-30 https://www.ysspatil.com/papers/2017/7/12/emergent-phases-and-novel-critical-behavior-in-a-non-markovian-open-quantum-system monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1499837319378-UWUQC744UTDGAMO42X4B/Figure+1-01.png Papers - Emergent phases and novel critical behavior in a non-Markovian open quantum system - Figure 1 (a) Schematic of the two-mode system. (b) The phase diagram as a function of the drive strength \(\mu \equiv F_P/F_{cr}\) and the normalized reservoir decay rate \((\gamma_0 \tau_r)^{-1}\). The color scale indicates the least negative real part of the eigenvalues of the susceptibility matrix (see text). Critical points and phase boundaries (dashed lines) correspond to the vanishing of this real part, i.e. a divergent relaxation time. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1499837321495-1YH8G8LWTC2KMC654U93/Figure+2-01.png Papers - Emergent phases and novel critical behavior in a non-Markovian open quantum system - Figure 2 The transition between the \(U(1)\) and the \(U(1) \times \mathbb{Z}_2\) phase versus the normalized reservoir decay rate, \((\gamma_0 \tau_r)^{-1}\) The critical point occurs at \((\gamma_0 \tau_r)^{-1} = \frac{1}{2}\), corresponding to a divergent variance, \(\mathrm{Var}(\dot{\phi})\), of the instantaneous frequency of the signal and idler modes. Below this critical point, these modes no longer self-oscillate at their nominal resonances but shift to \(\omega_{i} \rightarrow \omega_i \pm \Delta, \omega_{s} \rightarrow \omega_s \mp \Delta\), corresponding to a breaking of the \(\mathbb{Z}_2\) symmetry (see inset, bottom). In contrast to the spontaneously chosen but constant phase difference between the two modes in the \(U(1)\) phase, the phases of these modes now oscillate (see inset, top) at a frequency \(\Delta\) that continuously grows from zero below the critical point. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1499837323172-AZAK6SRKTR0QY0OG2USH/Figure+3-01.png Papers - Emergent phases and novel critical behavior in a non-Markovian open quantum system - Figure 3 The behavior of the low lying eigenspectrum corresponding to the disordered phase (orange), \(U(1)\) phase (green) and \(U(1) \times \mathbb{Z}_2\) phase (blue) with increasing reservoir coherence time \(\tau_r\) showing the relative positions of the exceptional point (blue circle) and the critical point (green circle) {\em vs} the drive strength. The imaginary part of the eigenvalue is represented as the width of the eigenmode. The exceptional point corresponds to a coalescence of the eigenvalues and eigenmodes and a vanishing imaginary part. The critical point occurs when the disordered phase becomes unstable (\(\mathrm{Re}[\lambda] >0\)) and gives way to the broken symmetry phases. (a) In the Markovian regime, i.e. \((\gamma_0 \tau_r)^{-1} \gg \frac{1}{2}\), the exceptional point occurs before the critical point governing the transition to the \(U(1)\) phase. The eigenvalues are purely real in the vicinity of the critical point. (b) At \((\gamma_0 \tau_r)^{-1} = \frac{1}{2}\), the exceptional point and the critical point coincide, i.e. the real and imaginary parts of the eigenvalues vanish simultaneously at the critical point, indicating the emergence of the \(U(1) \times \mathbb{Z}_2\) phase. (c) Deep in the non-Markovian regime, i.e. \((\gamma_0 \tau_r)^{-1} \ll \frac{1}{2}\), the critical point occurs before the exceptional point and the transition to the \(U(1) \times \mathbb{Z}_2\) phase occurs when the eigenvalues are purely imaginary. The displayed eigenspectra correspond to (a) \((\gamma_0 \tau_r)^{-1} = 1.25\), (b) \((\gamma_0 \tau_r)^{-1} = 0.50\), and (c) \((\gamma_0 \tau_r)^{-1} = 0.15\). https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1499837326700-C8SZ937W7LZEYY54NXS6/Figure+4-01.png Papers - Emergent phases and novel critical behavior in a non-Markovian open quantum system - Figure 4 (Top) The logarithmic negativity \(\mathcal{E}_N\) as a measure of the bipartite entanglement \cite{peres1996, plenio2005} between the signal and idler modes {\em vs} the drive strength \(\mu\) and the normalized reservoir decay rate \((\gamma_0 \tau_r)^{-1}\). (Bottom) In the \(U(1) \times \mathbb{Z}_2\) phase, the entanglement between the two modes extends well beyond the quantum regime and can be observed even for large thermal occupancy of the two modes. The logarithmic negativity is shown for increasing thermal occupancy \(\bar{n}_{th}\) {\em vs} drive strength for \((\gamma_0 \tau_r)^{-1}= \frac{1}{5}\). For comparison, the logarithmic negativity for a Markovian system with \(\bar{n}_{th} = 5\) is shown in dashed lines. https://www.ysspatil.com/papers/2016/1/10/nonlinear-phonon-interferometry-at-the-heisenberg-limit monthly 0.5 2025-04-07 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1452587211125-IU1DJACG8D4RLRQ0FU59/Figure1.png Papers - Nonlinear phonon interferometry at the Heisenberg limit - Figure 1 A \(SU(1,1)\) phonon interferometer. (a) The two arms of the interferometer are distinct mechanical modes at frequences \(\omega_s\) and \(\omega_i\). A parametric amplifier interaction (PA) between the two modes generates strong correlations between these modes. A phase shift of interest \(\varphi\) is then imparted to the signal mode. A timed and pulsed beam splitter interaction (BS) between the modes coherently mixes the two correlated arms resulting in reduced quadrature noise at the outputs. (b) The timing sequence : The input to the interferometer is the coherent state \(|\alpha_s,0\rangle\) prepared at \(t<0\). The signal and idler get correlated during the parametric amplifier pulse for time \(t_{PA}\). After a variable interaction period, the two modes are coherently mixed by the beam splitter pulse for time \(t_{BS}\), followed by a weak measurement of the output modes. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1452587209181-SSWIPD3F2CLV50DOUZ3Q/Figure2V2.png Papers - Nonlinear phonon interferometry at the Heisenberg limit - Figure 2 The parametric amplifier phase diagram. (a) Two-mode squeezing below and above the instability threshold (\(\mu=1\)): normalized standard deviations of squeezed (red) and amplified (blue) cross-quadratures. The solid lines are no-free-parameter predictions of our model with independently measured damping rates and eigenfrequencies, taking into account finite measurement time and differential substrate temperature effects (see SI). (b) Steady state amplitudes of the signal and idler modes show a power-law growth of \(0.53\pm0.03\) consistent with the prediction of \(0.5\). The exponential growth rate of the signal idler motions increases linearly with parametric amplifier actuation \(\mu\). (All signal and idler motions are normalized to their respective thermal motions.) https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1452587210803-9FUTXKE2RANLIDI7PQ28/Figure3.png Papers - Nonlinear phonon interferometry at the Heisenberg limit - Figure 3 Enhanced transient squeezing -- phase space distribution and squeezing dynamics. By transient application of the parametric interaction, two-mode squeezing beyond the steady-state bound of 3 dB can be achieved (see main text). (a) Phase space distribution of \(15.4\pm0.3\)dB squeezed states -- \((x_s,x_i)\) (red) and \((y_s,y_i)\) (blue). The thermal state (grey) is shown for reference. (b,c) Dynamics of growth and decay of the two-mode squeezed state in units of the mechanical damping time \(2 \gamma^{-1}\). The parametric amplifier is driven transiently with strength \(\mu = 38(5)\), and the quadrature variance of 236 iterations is plotted vs time. For comparison, the steady state bound of 3 dB is indicated in grey. The shaded regions represent no-free-parameter bounds due to variations in the parametric drive \(\mu\) across the iterations. (All signal and idler displacements have been normalized to their respective thermal amplitudes measured at \(t=0\).) https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1452587211550-G7EF5GAJ0FH22HOLRAKG/Figure4.png Papers - Nonlinear phonon interferometry at the Heisenberg limit - Figure 4 The Heisenberg scaling of phase sensing in the nonlinear phonon interferometer is shown vs the phonon number gain \(G^2\). The shot noise limit for conventional interferometry, i.e. in the absence of two-mode correlations, is shown for comparison (blue). The data correspond to the experimental parameters of Fig. 3. The shaded regions represent no-free-parameter bounds due to variations in the parametric drive \(\mu\) across the iterations. Inset: The phonon interferometer's estimated scaling exponent \(\alpha\) for the phase sensitivity, \(\delta \phi \sim 1/N^\alpha\), is shown as a function of the parametric drive \(\mu\) and the parametric pulse duration \(t_{PA}\), indicating the transition from SQL scaling (\(\alpha = 1/2\)) to Heisenberg scaling (\(\alpha = 1\)) as \(t_{PA}\) is reduced (see text). https://www.ysspatil.com/papers/measurement-induced-localization-of-an-ultracold-lattice-gas monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451874651208-9RLC9V1G0ASIF8GVDY4P/Fig+1Exp.png Papers - Measurement-induced localization of an ultracold lattice gas - Figure 1 (a) Lattice imaging scheme: An atom within a lattice site is cooled to the ground state |D⟩≡|F=1,mF=+1;ν=0⟩ via RSC. This state is nominally a “dark state”; i.e., it does not emit fluorescence. An auxiliary “imaging” beam promotes the atom out of this state to a fluorescing state |B⟩ which is subsequently cooled back to |D⟩. Repeated cycles of this process extract fluorescence from the atom while continually restoring the atom to |D⟩. (b) The imaging scheme thus allows us to distinguish between two possible states of the atom—a bright state |B⟩ that can be imaged and a dark state |D⟩ that cannot be imaged. (c) Fluorescence images of a lattice gas obtained at increasing levels of the measurement rate Γm. The field of view of each frame is 250 μm×250 μm. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451874672660-UL2BHS8HMYF3F0BCN9H3/Fig+2Exp.png Papers - Measurement-induced localization of an ultracold lattice gas - Figure 2 Photoassociation measurements demonstrating the crossover from the weak measurement regime (Γm≪J) to the strong measurement regime (Γm≫J). In the former regime (a), position measurements have little influence on tunneling, and the two-body lifetime τ = 1/κ is independent of the imaging rate. In the latter regime (b), measurement-induced localization suppresses tunneling rates leading to an increase of the two-body lifetime. (c) Measurements of two-body lifetime vs measurement rate. These data were obtained at a lattice parameter s=8.5(2.0) with τ0=31(3) ms. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451874698455-KORKXC2CSV3GG7S6OFN7/Fig+3Exp.png Papers - Measurement-induced localization of an ultracold lattice gas - Figure 3 In the strong measurement regime, the effective tunneling rate is given by Jeff∼J^2/Γm. This leads to a two-body lifetime τ = 1/κ that linearly increases [as seen in (a)] with the measurement rate—a clear signature of the QZE. These data were obtained for s=23(2). (b) The quadratic scaling of the effective tunneling rate (and, hence, the photoassociation rate κ) with the bare lattice tunneling rate is demonstrated by measurements of κ for lattice gases confined in different lattice depths. These data were obtained by imaging the lattice gases at fixed measurement rate Γm. The dashed line shows a quadratic fit to the data. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451874712560-IKG3W0FGQN49QKKQI5SH/Fig+4Exp.png Papers - Measurement-induced localization of an ultracold lattice gas - Figure 4 Suppression of atomic diffusion due to position measurements. A brief on-resonant optical pulse depletes the central region of the lattice gas [indicated by the arrow in (a)]. (b) Cross section of the atomic ensemble following this pulse. (c) Atoms rapidly diffuse into this central region in the absence of imaging (blue, s=8.5, Γm=0). In contrast, diffusion is suppressed when the atoms are continuously imaged (red, s=8.5, Γm=1000 per s). https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451874729121-Q4NOAS6T9OWZ3M93Z3B4/Fig+5Exp.png Papers - Measurement-induced localization of an ultracold lattice gas - Figure 5 For measurement rates Γm that exceed the Raman cooling rate ΓRSC, atoms are promoted to higher vibrational bands because of the measurement. The increased tunneling rates in these higher bands cause a deviation from the linear scaling of the lifetime τ with Γm. Because of the proportionate relation between the Raman cooling rate and the lattice depth, this deviation occurs more readily for atoms in shallow lattices. The data shown represent two-body lifetimes in the Zeno regime for lattice parameters s=9.5(1.5), (filled square), s=21(2), (filled circle). The shaded region represents a Monte Carlo simulation of a kinetic model of the measurement process. Inset: Simulated two-body lifetimes vs measurement rate: The onset of higher-band tunneling occurs at larger Γm for increasing Raman cooling rates (bottom to top). https://www.ysspatil.com/papers/thermomechanical-two-mode-squeezing-in-an-ultrahigh-q-membrane-resonator monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451871740909-63DZT150DY3CSWQVWXYN/Figure1CaptureExp.PNG Papers - Thermomechanical two-mode squeezing in an ultrahigh Q membrane resonator - Figure 1 (a) The resonator consists of a high-stress silicon nitride membrane deposited on a silicon substrate. Distinct eigenmodes of the membrane resonator (representative eigenfunctions shown) with frequencies ωi,jare coupled via a substrate-mediated interaction. This two-mode interaction can be controlled by actuating the substrate to an amplitude XS at frequencies close to ωi+ωj. (b) Experimental schematic: Mechanical motion of the membrane is optically detected in a Michelson interferometer, with the two membrane modes (i,j) distinguished by phase-sensitive lock-in detection. The eigenfrequency of a third, high-Q mechanical mode is continuously monitored and acts as a mechanical “thermometer.” The resonator modes are actively frequency stabilized to this thermometer mode by photothermal feedback. In the presence of this feedback, the frequency stability of each resonator mode is better than 1 ppb over 1000 seconds. ECDL–External cavity diode laser; AOM–Acousto-optic modulator; PID–Proportional-Integral-Derivative controller. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451871737129-T2Y3HHKXQROQ8PI6X3L9/Figure2CaptureExp.PNG Papers - Thermomechanical two-mode squeezing in an ultrahigh Q membrane resonator - Figure 2 (a) Parametric amplification of a membrane mode due to actuation of the substrate. The vertical line indicates the threshold for parametric instability. The solid green line indicates the thermomechanical amplitude of the membrane mode. The dashed gray line shows the detection noise floor. (b) In the absence of the parametric drive, large amplitude oscillations of either membrane mode (xi) result in increased dissipation (and a lower quality factor Qj) of the other mode due to up-conversion of excitations into the substrate. The variation of the normalized dissipation (Qj/Qj,0), shown above for various pairs of coupled modes, is well described by a characteristic length scale ξ(see text). (c) The linear dependence of the length scale ξ [extracted from data such as shown in (b)] vs the threshold amplitude for parametric instability, as predicted by the two-mode model. See Supplemental Material [30] for details of the various modes depicted above. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451871738872-QZI1U73Q0SAB1303R709/Figure3CaptureExp.PNG Papers - Thermomechanical two-mode squeezing in an ultrahigh Q membrane resonator - Figure 3 Phase-sensitive amplification, Gj(ϕ), vs the phase of the pump excitation. Data shown correspond to normalized pump amplitudes μ=XS/XS,th=0,0.021,0.038,0.042,0.086,0.13(red, blue, green, black, cyan, orange). For these data, the threshold for parametric self-oscillation corresponds to XS=40 fm, the signal and idler modes are driven to 35sqrt(kBT/mωj^2) and 400sqrt(kBT/mωi^2), respectively, corresponding to η=14.4. Inset: Estimate of the pump amplitude from fits to these data agree with the actual pump amplitude to within 5%. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451871735995-NEPCG8ZWJXIK0WGBKRW7/Figure4CaptureExp.PNG Papers - Thermomechanical two-mode squeezing in an ultrahigh Q membrane resonator - Figure 4 Steady-state thermomechanical two-mode squeezing. Left: Phase space distributions of the quadratures αi,αj in the absence (blue) and presence (red) of the pump field, showing the emergence of correlations, i.e., noise squeezing, due to nondegenerate parametric amplification. Right: The standard deviations of the cross-quadratures xa,yb(red, blue), (amplified) and xb,ya (red, blue) (squeezed) vs pump amplitude. The shaded curves indicate the no-free-parameter prediction of our noise squeezing model based on independently measured parameters of our system. The green trace represents the expected degree of squeezing taking into account a finite measurement duration (see Supplemental Material [30]). https://www.ysspatil.com/papers/multimode-phononic-correlations-in-a-nondegenerate-parametric-amplifier monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883472232-19NSVV7OK9A42GMCAU8T/Fig1Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 1 (a) Distinct eigenmodes of the membrane resonator are coupled through parametric excitation of the supporting substrate. (b) The strength of the two-mode interaction is enhancedwhen the parametric interaction betweenmembrane eigenmodes at ωi,j is mediated by a substrate excitation at ωS = ωi + ωj . https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883472260-Z7RTAJHH78IK0R8O2859/Fig2Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 2 Pump (blue) and signal/idler (red) amplitudes as a function of the normalized parametric drive, μ =|Fs|/|Fs,cr|. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883474375-SRI3G8TZLGXXJ4YHO8Y8/Fig3Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 3 Normalized variances of amplified and squeezed collective quadratures as a function of the normalized parametric drive. Black lines indicate the variances formatched frequencies (δω = 0 ) and loss rates (δγ = 0). Solid lines indicate the amplified (blue) and squeezed (red) variances for δγ = 0.5, δω = −0.5. The dashed lines indicate the amplified and squeezed variances for δγ = δω ≠ 0, the case ofmatched asymmetrieswhere the peak noise squeezing again approaches a factor of 1/2 as μ → 1. The dashed horizontal line represents the thermomechanical variance given by kBT/mω^2. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883480663-0G6N9AOQ1Z6QOIKTGT4T/Fig4Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 4 (a) Peak noise squeezing as a function of loss asymmetry δγ for δω = 0 with the squeezing going linearly from 1/2 → 1 as δγ = 0 → 1. (b) Peak squeezing as a function of the frequency asymmetry δω, for δγ = 0. (c) Peak squeezing as a function of δγ and δω. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883478763-VRGZSEJ1BUHLY3UGIUP5/Fig5Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 5 (a) Normalized variance of the fluctuations in the y+ (amplified, blue) and y− (squeezed, red) quadratures for the case of zero detuning (solid lines) and a detuning of Δ = γ (dashed lines). The amplified quadrature diverges at the instability threshold. For Δ = 0, this occurs at μ = 1 (solid black vertical line). For Δ = γ, this occurs at μ = sqrt(1 +(Δ/γ)^2) = sqrt(2) (dashed black vertical line). The black horizontal line is at 1/2. (b) Peak noise squeezing as a function of normalized detuning Δ/γ . Both these graphs are shown for the case of no loss or frequency asymmetry, i.e. δγ = δω = 0. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883481144-6ZLZ8NTGLABTXX9R5RL4/Fig6Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 6 Variance of the fluctuations in the difference y− (red) and sum y+ (blue) quadratures vs the parametric drive μ. The dashed lines are computed for δγ = δω = 0. The solid lines are computed for δγ = 0.31, δω = 0.09. The amplitude difference quadrature is squeezed for all values above threshold to a value of 1/2 . As can be seen, amplitude difference squeezing is extremely robust to experimental imperfections such as a frequency mismatch or loss asymmetry. Inset: schematic of the mean value of the membrane mode amplitude Ai,j and the fluctuations δαi,j and δβi,j . δβ represent amplitude fluctuations while δα are related to fluctuations of the phase. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883483346-GS73YTRRCJP7SGG2MQ6M/Fig7Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 7 Two-mode correlations in the vicinity of the threshold for parametric instability. Variance of the fluctuations of the normalized difference (y−) and sum (y+) quadratures above and below threshold vs the normalized parametric drive μ. The dashed lines represent the variances for δγ = δω = 0. The solid lines represent the variances for δγ = 0.31, δω = 0.09. The dashed horizontal line represents the thermomechanical variance given by kBT/mω^2. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451883483945-QQUXU5JIU9WR9CACLRHO/Fig8Exp.jpg Papers - Multimode phononic correlations in a nondegenerate parametric amplifier - Figure 8 Corrections to squeezing spectra due to finite measurement duration. Normalized variance of amplified (y+) and squeezed (y−) quadratures for a measurement time of 300 s (~100 ring down periods) (black solid lines). Also shown for comparison are the corresponding amplified (blue) and squeezed (red) quadratures in steady state. These are computed for δγ = 0.31, δω = 0.09 (γ ~ 2π × 100mHz) and correspond to the experimental parameters in [28]. The divergence at the instability threshold is attenuated for finite measurement times due to the divergent response times. https://www.ysspatil.com/papers/nondestructive-imaging-of-an-ultracold-lattice-gas monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451885884279-XS344N9VURHV2V5QOC28/Fig1Exp.PNG Papers - Nondestructive imaging of an ultracold lattice gas - Figure 1 (a) Lattice imaging scheme: An atom within a lattice site is cooled to the ground state |g⟩≡|F=1,mF=+1;ν=0⟩ via RSC. An auxiliary imaging beam promotes the atom out of this state to a fluorescing state, which is subsequently cooled back to |g⟩. Repeated cycles of this process extract fluorescence from the atom while continually restoring the atom to |g⟩; (b) The near-resonance optical fields used in the imaging sequence. A cooling beam (RSC) with σ+ and π components cools and optically pumps the atom into the dark state |g⟩. A σ− beam induces fluorescence by bringing the atom out of the dark state. (c) Raman fluorescence image of a gas of 1.5×10^6 atoms obtained within 15 ms. The field of view is 250μm × 250μm. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451885882281-V6LDPBOYHQ9HLYFK6IV4/Fig2Exp.PNG Papers - Nondestructive imaging of an ultracold lattice gas - Figure 2 Spatially resolved sideband spectroscopy of the lattice gas following the imaging sequence yielding ⟨n⟩=0.01+0.03−0.01. Inset: A time-of-flight absorption image of the ultracold gas following an intense interrogation pulse at the two-photon resonance. The divot near the center of the atomic distribution shows the location and relative size of the beams used for sideband spectroscopy. The field of view is 600 μm ×600 μm. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451885883911-1281149RLMUJQ6JTXQTP/Fig3Exp.PNG Papers - Nondestructive imaging of an ultracold lattice gas - Figure 3 Regimes of fluorescence acquisition rates for non-destructive imaging. (a) Measured temperature of the lattice gas in a pulsed imaging sequence, in units of the vibrational frequency ωL. The temperature during the fluorescence pulse grows (red) with increasing fluorescence rates while RSC rapidly cools the atoms back to the ground state (blue). (b) Measured atom number following the imaging sequence. At low fluorescence rates, the atom number is conserved indicating negligible levels of tunneling across sites. As the fluorescence rate is increased, the increasing temperature during the fluorescence pulse causes tunneling followed by light-induced loss. The shaded area represents the critical fluorescence rate for the onset of tunneling as identified by our measurements of light-induced loss. Inset: Evolution of atom number immediately following an intense fluorescence pulse (Γf=6×10^5 per s) shows that RSC quickly (within 100 μs) binds the atoms to the ground state of a lattice site thereby drastically suppressing tunneling. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451885885087-DNG0SXNFMTP4MFQA6W65/Fig4Exp.PNG Papers - Nondestructive imaging of an ultracold lattice gas - Figure 4 The fraction of atoms remaining after the imaging sequence (Nf/Ni) vs fluorescence rates for lattice depths of U0/Er=14.6,24.9,36.7 and 76.2 (left to right). Inset: An estimate of the maximum fluorescence acquisition rate Γf,max per atom vs s = U0/Er. https://www.ysspatil.com/papers/dissipation-in-ultrahigh-quality-factor-sin-membrane-resonator monthly 0.5 2022-01-30 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451887236282-CT2PZO4J0F315SZBZJ9G/Fig1Exp.PNG Papers - Dissipation in ultrahigh quality factor SiN membrane resonator - Figure 1 Peak mechanical quality factors of a L=5  mm, h=100  nm SiN membrane versus frequency (filled square). The solid line corresponds to f×Q = kB/h×300  K. For low mode frequencies (νjk < 300  kHz) , the quality factors can be improved by an order of magnitude (filled diamond) simply by reducing the contact region between the substrate and the in-vacuum mount. The weak frequency dependence of the measured Qs at high frequencies is further reduced for h=30  nm (opened square) (see text for discussion). Inset: characteristic mechanical ringdown of the (5,5) mode at ν55 = 407  kHz. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451887235029-N26D8LL178IMIEZOMM27/Fig2Exp.PNG Papers - Dissipation in ultrahigh quality factor SiN membrane resonator - Figure 2 Peak mechanical quality factors versus film geometry parametrized by the ratio of membrane width (L) to membrane thickness (h). For L/h<10^5, we observe a scaling consistent with Q∼(L/h)^2. A linear scaling is also shown for reference. https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451887250561-LZ0U2IFXY5JAQTWUKSZ2/Fig3Exp.PNG Papers - Dissipation in ultrahigh quality factor SiN membrane resonator - Figure 3 Interferometric imaging of the mechanical modes: in situ images of the (a) (1,10) mode and (b) (9,9) mode (color scale for displacement shown). Substrate-induced coupling between proximal asymmetric eigenmodes results in hybridization into more symmetric structures. (c),(d) The modal structures corresponding to ϕ10,6 ± ϕ6,10 hybridized modes. These can be compared to the calculated mode profiles for this hybridization (e),(f). https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1451887238075-DCZ07T84K6MOJE9RPRCU/Fig4Exp.PNG Papers - Dissipation in ultrahigh quality factor SiN membrane resonator - Figure 4 (a) Predicted quality factors versus mode indices based on asymptotic limits of our anchor loss model (see the Supplemental Material [25] for details), (b) Predicted quality factors versus ϕ ≡ arctan(j/k) for mode indices sqrt(j2+k2) = 12 with (without) substrate-mediated hybridization are shown as filled square (filled circle). Also shown is the asymptotic expression for the quality factors from our model (dashed line). (c) Measured Qs for mode indices indicated by the green arc in (a). (d) The angle-averaged measurements from (c) are compared to our predictions from (b). https://www.ysspatil.com/papers/2016/1/1/strong-field-spectral-interferometry-using-the-carrierenvelope-phase monthly 0.5 2021-11-27 https://www.ysspatil.com/thoughts daily 0.75 2016-09-24 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1452491318098-WRYC8FHMEDHZZQ0J8N1C/P1010164.JPG Think https://www.ysspatil.com/thoughts/2016/9/24/the-internet-as-an-engine-of-liberation-is-an-innocent-fraud monthly 0.5 2016-09-24 https://www.ysspatil.com/thoughts/2016/2/15/gravitational-waves monthly 0.5 2016-02-16 https://images.squarespace-cdn.com/content/v1/5680d83aa2bab84261fa56ba/1455527820371-SMTHPYDQDUGJFC3SCK5T/image-asset.png Think - Gravitational waves! The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filtered with a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain. GW150914 arrived first at L1 and 6.9+0.5−0.4  ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [37, 38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credible regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms [39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets [40, 41]. These reconstructions have a 94% overlap, as shown in [39]. Third row: Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series. 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