Non-equilibrium thermodynamics of harmonically trapped bosons

Abstract

We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the establishment of entanglement. We extend our analysis to multipartite systems by examining the case of three trapped atoms. We show the initial (pre-quench) interactions play a vital role in determining the dynamical features, while the qualitative features of the two particle case appear to remain valid. Finally, we propose the use of the atomic density profile as a readily accessible indicator of the non-equilibrium properties of the systems in question.

Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility

“…The number of non-zero eigenvalues is the Schmidt rank and if it is larger than 1, the two-particle state is entangled. The vNE can also be used as a measure of irreversibility in the system, similar to the irreversible work, and will therefore be affected by the quantum fluctuations induced by the non-adiabatic interaction ramp [43]. To quantify the ability of the STA to create correlations between the two particles we calculate the difference between the vNE at the end of the interaction ramp, S(t f ), and the vNE of the target equilibrium state S T…”

“…One can immediately notice the presence of distinct oscillations at longer times for the reference ramp, which are not present in the irreversible work. These can be attributed to the breathing dynamics of the two particles in the harmonic trap, where the particles periodically collide at the trap centre [43,[60][61][62]. In this process the separation between them is changed, which has a sizeable effect on the vNE and consequently on ∆S.…”

“…We consider the one-dimensional case and propose creating entanglement between these two particles through the design of a time-dependent Feshbach pulse [39][40][41][42]. While the hasty implementation of such a process can have unwanted consequences in relation to the creation of unwanted dynamical processes and fluctuating entanglement [43,44], we show that a suitably designed STA process can negate these effects even when it is carried out abruptly on short timescales. To design the form of the Feshbach pulse such that it fulfills the desired dynamical evolution of the interacting state we use an inverse engineering method by ultilizing a variational ansatz.…”

Spin–orbit coupling in the presence of strong atomic correlations

“…Our results are a useful contribution to the understanding of the emergent behaviour of quantum systems and the bridging of the gap between single and many-body states. The framework presented is also well suited to investigate these systems' dynamical properties [27][28][29].…”

Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion

“…The properties of the monopolar excitation have also been examined [32] upon quenching the trapping frequency of the harmonic oscillator. In the same context and referring to very strong interactions the dynamical orthogonality of the postquench state with respect to the initial one has been found [33]. Moreover, the dynamical generation of entanglement when considering low-energy collisions of the two atoms, each of them being initialized in a superposition of two counterpropagating wavepackets, has been investigated [34].…”