We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green\&$\#$39;s function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

}, url = {https://arxiv.org/abs/1803.05122}, author = {Ranchu Mathew and Eite Tiesinga} } @article {1999, title = {Phase-space mixing in dynamically unstable, integrable few-mode quantum systems}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/07/05}, pages = {013604}, abstract = {Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

}, doi = {10.1103/PhysRevA.96.013604}, url = {https://arxiv.org/abs/1705.01702}, author = {Ranchu Mathew and Eite Tiesinga} } @article {1304, title = {Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/09/03}, pages = {033602}, abstract = { We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop. }, doi = {10.1103/PhysRevA.92.033602}, url = {http://arxiv.org/abs/1506.09149v2}, author = {Ranchu Mathew and Avinash Kumar and Stephen Eckel and Fred Jendrzejewski and Gretchen K. Campbell and Mark Edwards and Eite Tiesinga} } @article {1272, title = {Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances }, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/5/10}, abstract = { We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85\% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal. }, doi = {10.1103/PhysRevA.87.053608}, url = {http://arxiv.org/abs/1301.4234v2}, author = {Ranchu Mathew and Eite Tiesinga} }