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arXiv:1712.04296 · Physical Review A

Phases of driven two-level systems with nonlocal dissipation

Christopher D. Parmee, Nigel R. Cooper

Published May 23, 2018• 43 citations
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Abstract

We study an array of two-level systems arranged on a lattice and illuminated by an external plane wave which drives a dipolar transition between the two energy levels. In this setup, the two-level systems are coupled by dipolar interactions and subject to nonlocal dissipation, and so behave as an open many-body quantum system. We investigate the long-time dynamics of the system at the mean-field level and use this to determine a phase diagram as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations, and phase bistabilities. We investigate these phases in more detail and explain how nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we discuss what features would survive in the full quantum description.

DOI
10.1103/physreva.97.053616

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We study an array of two-level systems arranged on a lattice and illuminated by an external plane wave which drives a dipolar transition between the two energy levels. In this setup, the two-level systems are coupled by dipolar interactions and subject to nonlocal dissipation, and so behave as an open many-body quantum system. We investigate the long-time dynamics of the system at the mean-field level and use this to determine a phase diagram as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations, and phase bistabilities. We investigate these phases in more detail and explain how nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we discuss what features would survive in the full quantum description.
We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and dissipation. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller mean field approximation for density matrices. The dissipative processes are engineered such that the system, in the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal long-range order. We investigate how the coherent interaction affects the properties of the steady state of the system qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state without long-range order. The phase diagram also exhibits an extended domain where an instability of the homogeneous steady state gives rise to a persistent density pattern with spontaneously broken translational symmetry. In the limit of low particle density, we provide a precise analytical description of the time evolution during the instability. Moreover, we investigate the transient following a quantum quench of the dissipative processes and we elucidate the prominent role played by collective topological variables in this regime.
In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin−1/2-1/2−1/2 models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.
We study theoretically a driven dissipative one-dimensional XXZ spin-1/2 chain with dipole coupling and a tunable strength of the Ising and XY interaction. Within a mean-field approximation, we find a rich phase diagram with uniform, spin density wave, antiferromagnetic and oscillatory phases, as well as regions of phase bistability. We study the phase diagram of small quantum systems using exact diagonalisation, and compare the results to the mean-field theory. We find that while expectation values only capture the uniform phases of the mean-field theory, fluctuations about these expectation values give signatures of spatially non-uniform phases and bistabilities. We find these signatures for all ratios of the Ising to XY interaction, showing that they appear to be general features of spin-1/2 systems.
Abstract We study theoretically a driven dissipative one-dimensional XXZ spin-1/2 chain with dipole coupling and a tunable strength of the Ising and XY interaction. Within a mean-field approximation, we find a rich phase diagram with uniform, spin density wave, antiferromagnetic and oscillatory phases, as well as regions of phase bistability. We study the phase diagram of small quantum systems using exact diagonalisation, and compare the results to the mean-field theory. We find that while expectation values only capture the uniform phases of the mean-field theory, fluctuations about these expectation values give signatures of spatially non-uniform phases and bistabilities. We find these signatures for all ratios of the Ising to XY interaction, showing that they appear to be general features of spin-1/2 systems.
We explore the synchronization phenomenon in the quantum few-body system of spins with the nonlocal dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized, which is revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in an infinite-size lattice by means of cluster mean-field approximation is also discussed.
We investigate the driven-dissipative dynamics of multilevel atomic arrays interacting via dipolar interactions at subwavelength spacings. Unlike two-level atoms in the weakly excited regime, multilevel atoms can become strongly entangled. The entanglement manifests as the growth of spin waves in the ground-state manifold and survives after turning off the drive. We propose the 2.9 μm transition between ^{3}P_{2}↔^{3}D_{3} in ^{88}Sr with 389 nm trapping light as a platform to test our predictions and explore many-body physics with light-matter interactions.