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Physical Review Letters

Laser-Induced Spatial Symmetry Breaking in Quantum and Classical Mechanics

Ignacio Franco, Paul W. Brumer

Published Jul 28, 2006• 31 citations
Publisher

Abstract

Phase-controllable transport in laser-irradiated spatially symmetric systems is shown to arise both quantum mechanically and classically from a common field-driven interference mechanism. Specifically, the quantum-to-classical transition for symmetry breaking in a quartic oscillator driven by an omega+2omega field is studied. For this, a double perturbation theory in the oscillator anharmonicity and external field strength, that admits an analytic classical limit, is carried out in the Heisenberg picture. The interferences responsible for the symmetry breaking are shown to survive in the classical limit and are the origins of classical control. Differences between reflection symmetry that plays a key role in the analysis, and parity that does not, are discussed.

DOI
10.1103/physrevlett.97.040402

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Phase-controllable transport in laser-irradiated spatially symmetric systems is shown to arise both quantum mechanically and classically from a common field-driven interference mechanism. Specifically, the quantum-to-classical transition for symmetry breaking in a quartic oscillator driven by an omega+2omega field is studied. For this, a double perturbation theory in the oscillator anharmonicity and external field strength, that admits an analytic classical limit, is carried out in the Heisenberg picture. The interferences responsible for the symmetry breaking are shown to survive in the classical limit and are the origins of classical control. Differences between reflection symmetry that plays a key role in the analysis, and parity that does not, are discussed.
Analysis of fundamentally open systems which exhibit both spatial reflection (parity) and time-reversal symmetry, called PT-symmetric [1] systems, has played an important role in understanding the dynamics of a broad class of non-Hermitian systems. Such systems support distinct regimes of stability and instability respectively, and the transition between these plays an important role in the system dynamics. We investigate a variety of non-Hermitian systems which exhibit a PT-symmetry breaking transition in both classical and quantum contexts using an array of theoretical and numerical approaches which are directly amenable to physical experiments. Organizationally, we divide these studies into those done on classical and quantum systems. Specifically for classical systems we analyze several interesting phenomena in the context of optical waveguide arrays. These provide an important testing ground for much of the discrete, PT-symmetric theory. In our case, we analyze PT-symmetric extensions of several interesting lattice models. Firstly, we explore single gain/loss pair, PT-symmetric extensions of the Su-Schreiffer-Heeger (SSH) model [2] and the Aubry-Andre-Harper (AAH) model [3,4]. In both cases, we find a veiled symmetry which is responsible for the PT-symmetry. Secondly we expand upon the Rudner-Levitov (RL) model [5,6], a non-Hermitian extension of the SSH model with multiple gain/loss pairs, and we explore the dependence of topological phenomena on changes in the initial state as well as their robustness in the presence of gain-induced nonlinearity. For quantum systems, we explore the rich PT-symmetric phase diagram resulting from time-periodic, Floquet PT-symmetry [7,8]. This is experimentally implementable in ultracold atomic systems [9], and features a reentrant PT-symmetric phase. Secondly, we examine quantum multi-photon statistics for a simple non-Hermitian model which is transformed and mapped to a system with unitary evolution via a unitary dilation, and is fully realizable on a small-scale quantum simulator [10].
The theory of spontaneous symmetry breaking---one of the cornerstones of modern condensed-matter physics---underlies the connection between a classically ordered object in the thermodynamic limit and its microscopic quantum-mechanical constituents. However, a large, but not infinitely large, system requires a finite symmetry-breaking perturbation to stabilize a symmetry-broken state over the exact quantum-mechanical ground state, respecting the symmetry. Here, we use the example of a particular antiferromagnetic model system to show that no matter how slowly such a symmetry-breaking perturbation is driven, the adiabatic limit can never be reached. Dynamically induced collective excitations---``quantum defects''---preempt the symmetry-breaking phenomenon and trigger the appearance of a symmetric nonequilibrium state that recursively collapses into the classical equilibrium state, breaking the symmetry at punctured times. The presence of this state allows ``quantum-classical'' transitions to be investigated and controlled in mesoscopic devices by externally supplying a proper dynamical symmetry-breaking perturbation.
Realizing and manipulating parity-time (PT\mathcal{PT}PT) symmetry in multidimensional systems are highly desirable for the exploration of nontrivial physics and the discovery of exotic phenomena in non-Hermitian systems. Finding non-Hermitian systems that still have all-real spectra even if their Hamiltonians possess only partial PT\mathcal{PT}PT symmetry has also attracted tremendous attention in recent years. Here, we report the experimental observation of partial PT\mathcal{PT}PT symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional partially PT\mathcal{PT}PT-symmetric optical potential for a probe laser beam is created. A transition of the partial PT\mathcal{PT}PT symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and nonpartial PT\mathcal{PT}PT phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the exceptional point location of the partial PT\mathcal{PT}PT symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing light amplifiers and attenuators in different parts of laser beams.
The effect of \mathcal{PT} 𝒫 𝒯 -symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of \mathcal{PT} 𝒫 𝒯 symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected \mathcal{PT} 𝒫 𝒯 -symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT} 𝒫 𝒯 -symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.
The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. This work finds a continuous phase transition when disorder breaks permutation symmetry, with details of the transition being controlled by the degree of chaos in the clean limit. The system changes from an area law entangled phase in the permutation symmetric subspace where collective variables exist to volume law entanglement in the full Hilbert space, beyond a critical strength of the disorder. This has potential implications for general many body physics, as well as technologies such as transmon qubits.
The quantum domain behaviour of a classical double-well oscillator which exhibits chaos in the presence of an external monochromatic field has been studied using Bohmian mechanics. The classical Kolmogorov-Arnol'd-Moser (KAM) tori break down in the presence of an external perturbation for which the corresponding quantal phase portrait exhibits regular islands owing to the quantum suppression of the classical chaos. It has also been observed that the classical chaos generally enhances the quantum fluctuations.