Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChaos and $mathcal{PT}$-symmetry breaking transitions in a driven, nonlinear dimer with balanced gain and loss
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Dynamics of a simple system, such as a two-state (dimer) model, are dramatically changed in the presence of interactions and external driving, and the resultant unitary dynamics show both regular and chaotic regions. We investigate the non-unitary dynamics of such a dimer in the presence of balanced gain and loss for the two states, i.e. a $mathcal{PT}$ symmetric dimer. We find that at low and high driving frequencies, the $mathcal{PT}$-symmetric dimer motion continues to be regular, and the system is in the $mathcal{PT}$-symmetric state. On that other hand, for intermediate driving frequency, the system shows chaotic motion, and is usually in the $mathcal{PT}$-symmetry broken state. Our results elucidate the interplay between the $mathcal{PT}$-symmetry breaking transitions and regular-chaotic transitions in an experimentally accessible toy model.
rate research
Read More
Balanced gain and loss renders the mean-field description of Bose-Einstein condensates PT symmetric. However, any experimental realization has to deal with unbalancing in the gain and loss contributions breaking the PT symmetry. We will show that such an asymmetry does not necessarily lead to a system without a stable mean-field ground state. Indeed, by exploiting the nonlinear properties of the condensate, a small asymmetry can stabilize the system even further due to a self-regulation of the particle number.
We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex $mathcal{PT}$-symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow for an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to non-vortex states. In addition, we study the influences of $mathcal{PT}$ symmetry on the dynamics of non-stationary vortex states placed at off-center positions.
Parity-time ($mathcal{PT}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $mathcal{PT}$-symmetric Hamiltonian change from real to complex conjugates at a critical value of gain-loss strength that is called the $mathcal{PT}$ breaking threshold. Here, we obtain the $mathcal{PT}$-threshold for a one-dimensional, finite Kitaev chain -- a prototype for a p-wave superconductor -- in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, on-site potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev mo del. In particular, for an even chain with zero on-site potential, we find a re-entrant $mathcal{PT}$-symmetric phase bounded by second-order EP contours. Our numerical results are supplemented by analytical calculations for small system sizes.
We present a quantum master equation describing a Bose-Einstein condensate with particle loss on one lattice site and particle gain on the other lattice site whose mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii equation. It is shown that the characteristic properties of PT-symmetric systems, such as the existence of stationary states and the phase shift of pulses between two lattice sites, are also found in the many-particle system. Visualizing the dynamics on a Bloch sphere allows us to compare the complete dynamics of the master equation with that of the Gross-Pitaevskii equation. We find that even for a relatively small number of particles the dynamics are in excellent agreement and the master equation with balanced gain and loss is indeed an appropriate many-particle description of a PT-symmetric Bose-Einstein condensate.
In this work we present a new generic feature of PT-symmetric Bose-Einstein condensates by studying the many-particle description of a two-mode condensate with balanced gain and loss. This is achieved using a master equation in Lindblad form whose mean-field limit is a PT-symmetric Gross-Pitaevskii equation. It is shown that the purity of the condensate periodically drops to small values but then is nearly completely restored. This has a direct impact on the average contrast in interference experiments which cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
