Person:

Dalla Torre, Emanuele

We consider a quantum quench in which two initially independent condensates are suddenly coupled and study the subsequent “rephasing” dynamics. For weak tunneling couplings, the time evolution of physical observables is predicted to follow universal scaling laws, connecting the short-time dynamics to the long-time nonperturbative regime. We first present a two-mode model valid in two and three dimensions and then move to one dimension, where the problem is described by a gapped sine-Gordon theory. Combining analytical and numerical methods, we compute universal time-dependent expectation values, allowing a quantitative comparison with future experiments.

We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an e↵ective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated su- perradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach, that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number of atoms N. For finite N, the photon mode behaves as a damped, classical non-linear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms’ depolarization due to dissipative dephasing.

We present and analyze a new approach for the generation of atomic spin-squeezed states. Our method involves the collective coupling of an atomic ensemble to a decaying mode of an open optical cavity. We demonstrate the existence of a collective atomic dark state, decoupled from the radiation field. By explicitly constructing this state we find that it can feature spin squeezing bounded only by the Heisenberg limit. We show that such dark states can be deterministically prepared via dissipative means, thus turning dissipation into a resource for entanglement. The scaling of the phase sensitivity taking realistic imperfections into account is discussed.

We consider the dynamics of a Bose-Einstein condensate with two internal states, coupled through a coherent drive. We focus on a specific quench protocol, in which the sign of the coupling field is suddenly changed. At a mean-field level, the system is transferred from a minimum to a maximum of the coupling energy and can remain dynamically stable, in spite of the development of negative-frequency modes. In the presence of a nonzero detuning between the two states, the “charge” and “spin” modes couple, giving rise to an unstable avoided crossing. This phenomenon is generic to systems with two dispersing modes away from equilibrium and constitutes an example of class-Io nonequilibrium pattern formation in quantum systems.