Quantum Matters

E. Pazy, I. Tikhonenkov, Y. B. Band, M. Fleischhauer, and A. Vardi, Nonlinear adiabatic passage from fermion atoms to boson molecules, Phys. Rev. Lett. 95, 170403 (2005)

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction Γ on the sweep rate α varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, Γ∝α, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Γ∝α1/3 when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.

H. Buljan, M. Segev, and A. Vardi, Incoherent Matter-wave solitons and pairing instability in an attractively interacting Bose-Einstein condensate, Phys. Rev. Lett. 95, 180401 (2005)

The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.

I. Tikhonenkov, E. Pazy, Y. B. Band, M. Fleischhauer, and A. Vardi, Many-body effects on adiabatic passage through Feshbach resonances, Phys. Rev. A 73, 043605 (2006)

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Γ on sweep rate α, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law Γ∝α is obtained when the initial molecular fraction is smaller than the 1∕N quantum fluctuations, and a cubic-root power law Γ∝α1∕3 is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.

M. Chuchem, K. Smith-Mannschott, M. Hiller, T. Kottos, A. Vardi, and D. Cohen, Quantum dynamics in the bosonic Josephson junction, Phys. Rev. A 82, 053617 (2010)

We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between the two condensates. For initially incoherent condensates, we find a universal value for the buildup of coherence in the Josephson regime. In addition, we contrast two seemingly similar on-separatrix coherent preparations, finding striking differences in their convergence to classicality as the number of particles increases.

I. Tikhonenkov, M. G. Moore, and A. Vardi, Optimal Gaussian squeezed states for atom interferometry in the presence of phase-diffusion, Phys. Rev A 82, 043624 (2010)

We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states in the presence interactions. For weak interactions, our results coincide with those of Huang and Moore [Y. P. Huang and M. G. Moore, Phys. Rev. Lett. 100, 250406 (2008)], with an optimal initial number variance σo∝N1/3 and an optimal signal-to-noise ratio so∝N2/3 for the total atom number N. As the interaction strength u increases past unity, phase diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number squeezing to initial phase squeezing with σo∝√uN and so∝√N/u shot-noise scaling. The initial phase squeezing translates into hold-time number squeezing, which is less sensitive to interactions than coherent states and improves so by a factor of √u.

I. Tikhonenkov, M. G. Moore, and A. Vardi, Robust sub-shot-noise measurement via Rabi-Josephson oscillations in bimodal Bose-Einstein condensates, Phys. Rev. A 83, 063628 (2011)

Mach-Zehnder atom interferometry requires hold-time phase squeezing to attain readout accuracy below the standard quantum limit. This increases its sensitivity to phase diffusion, restoring shot-noise scaling of the optimal signal-to-noise ratio in the presence of interactions. The contradiction between the preparations required for readout accuracy and robustness to interactions is removed by monitoring Rabi-Josephson oscillations instead of relative-phase oscillations during signal acquisition. Optimizing the signal-to-noise ratio with a Gaussian squeezed input, we find that hold-time number squeezing satisfies both demands and that sub-shot-noise scaling is retained even for strong interactions.

C. Khripkov and A. Vardi, Quantum Zeno control of coherent dissociation, Phys. Rev. A 84, 021606(R) (2011)

We study the effect of dephasing on the coherent dissociation dynamics of an atom-molecule Bose-Einstein condensate. We show that when phase-noise intensity is strong with respect to the inverse correlation time of the stimulated process, dissociation is suppressed via a Bose enhanced quantum Zeno effect. This is complementary to the quantum Zeno control of phase-diffusion in a bimodal condensate by symmetric noise [Phys. Rev. Lett. 100, 220403 (2008)] in that the controlled process here is phase formation and the required decoherence mechanism for its suppression is purely phase noise.

C. Khripkov, A. Vardi, and D. Cohen, Squeezing in driven bimodal Bose-Einstein condensates: Erratic driving versus noise, Phys. Rev. A 85, 053632 (2012)

We study the interplay of squeezing and phase randomization near the hyperbolic instability of a two-site Bose-Hubbard model in the Josephson interaction regime. We obtain results for the quantum Zeno suppression of squeezing far beyond the previously found short time behavior. More importantly, we contrast the expected outcome with the case where randomization is induced by erratic driving with the same fluctuations as the quantum noise source, finding significant differences. These are related to the distribution of the squeezing factor, which has log-normal characteristics: hence its average is significantly different from its median due to the occurrence of rare events.

C. Khripkov, D. Cohen, and A. Vardi, Coherence dynamics of kicked Bose-Hubbard dimers: Interferometric signatures of chaos, Phys. Rev. E 87, 012910 (2013)

We study the coherence dynamics of a kicked two-mode Bose-Hubbard model starting with an arbitrary coherent spin preparation. For preparations in the chaotic regions of phase space we find a generic behavior with Floquet participation numbers that scale as the entire N-particle Hilbert space, leading to a rapid loss of single-particle coherence. However, the chaotic behavior is not uniform throughout the chaotic sea and unique statistics is found for preparations at the vicinity of hyperbolic points that are embedded in it. This is contrasted with the low log(N) participation that is responsible for the revivals in the vicinity of isolated hyperbolic instabilities.

R. Bürkle, A. Vardi, D. Cohen, and J. R. Anglin, Probabilistic Hysteresis in Integrable and Chaotic Isolated Hamiltonian Systems, Phys. Rev. Lett. 123, 114101 (2019)

R. Bürkle, A. Vardi, D. Cohen, and J. R. Anglin, How to probe the microscopic onset of irreversibility with ultracold atoms, Sci. Rep. 9, 14169 (2019)

The microscopic onset of irreversibility is finally becoming an experimental subject. Recent experiments on microscopic open and even isolated systems have measured statistical properties associated with entropy production, and hysteresis-like phenomena have been seen in cold atom systems with dissipation (i.e. effectively open systems coupled to macroscopic reservoirs). Here we show how experiments on isolated systems of ultracold atoms can show dramatic irreversibility like cooking an egg. In our proposed experiments, a slow forward-and-back parameter sweep will sometimes fail to return the system close to its initial state. This probabilistic hysteresis is due to the same non-adiabatic spreading and ergodic mixing in phase space that explains macroscopic irreversibility, but realized without dynamical chaos; moreover this fundamental mechanism quantitatively determines the probability of return to the initial state as a function of tunable parameters in the proposed experiments. Matching the predicted curve of return probability will be a conclusive experimental demonstration of the microscopic onset of irreversibility.

C. Khripkov, A. Vardi, and D. Cohen, Many-body dynamical localization and thermalization, Phys. Rev. A 101, 043603 (2020)

We show that a quantum dynamical localization effect can be observed in a generic thermalization process of two weakly coupled chaotic subsystems. Specifically, our model consists of the minimal experimentally relevant subsystems that exhibit chaos, which are 3-site Bose-Hubbard units. Due to the high dimensionality of the composite 6-site system, the quantum localization effect is weak and cannot be resolved merely by the breakdown of quantum-to-classical correspondence. Instead, we adopt an intrinsic definition of localization as the memory of initial conditions, which is not related to the underlying classical dynamics. We discuss the dynamics in the chaotic sea, and in the vicinity of the mobility edge, beyond which ergodization is suppressed.

S. Ray, D. Cohen, and A. Vardi, Chaos induced breakdown of Bose-Hubbard modeling, Phys. Rev. A 101, 013624 (2020)

We show that the Bose-Hubbard approximation fails due to the emergence of chaos, even when excited modes are far detuned and the standard validity condition is satisfied. This is formally identical to the Melnikov-Arnold analysis of the stochastic pump model. Previous numerical observations of Bose-Hubbard breakdown are precisely reproduced by our simple model and can be attributed to many-body enhancement of chaos.

A. Dey and A. Vardi, Interaction-induced instability and chaos in the photoassociative stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates, Phys. Rev. A 101, 053627 (2020)

We study the effect of interactions on the conversion of atomic-to-molecular Bose-Einstein condensates via stimulated Raman adiabatic passage. Both energetic instability during avoided crossings and dynamical instability during chaotic intervals limit adiabaticity and impose low sweep-rate boundaries on the efficiency of the process. For the diabatic traverse of avoided crossings, we find a reciprocal power-law dependence of the final unconverted population on sweep rate. For the traverse of chaos, we find a sharp low-rate boundary determined by the dynamical instability parameters. The interplay of these two mechanisms determines which instability controls the failure of molecular production. A judicious choice of sweep parameters is hence required to restore the process efficiency.

S. Ray, J. R. Anglin, and A. Vardi, Prethermalization with negative specific heat, Phys. Rev. E 102, 052107 (2020)

We study noncanonical relaxation in an aggregate of subsystems with negative specific heat. The Thirring instability drives the constituent subsystems towards the edges of their energy spectrum, so that the existence of a single adiabatic invariant results in structured noncanonical steady states that are spectacularly different from the grand-canonical prediction. For parameter regimes where this adiabatic invariance breaks down, the system exhibits prethermalization far away from integrability, with an unprecedented contrast between the prethermal- and thermal states.