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arXiv:2404.10131 · Physical Review Research

Rotational superradiance in a time-reversal symmetry-broken quantum gas inside an optical cavity

Natalia Masalaeva, Farokh Mivehvar

Published Feb 18, 2025• 3 citations
arXivHTMLPDF

Abstract

The appearance of quantized vortices in a superfluid and a Bose-Einstein condensate (BEC) stems from their nontrivial response to time-reversal symmetry (TRS). Here, we show that breaking of the TRS by, for example, rotation or an external synthetic magnetic field in a transversely driven BEC coupled to a single mode of an optical cavity modifies drastically Dicke superradiance and self-ordering phenomena in this system. In particular, photon scattering from the pump laser into the cavity is amplified by rotational motion of the BEC, leading to so-called “rotational superradiance”—in a loose analogy to black-hole physics—with distinct critical scaling properties. In turn, cavity photons mediate long-range, periodic attractive interactions among the vortices, which compete with pairwise logarithmic repulsive vortex interactions and deform the Abrikosov triangular vortex lattice favoring a stripe-like pattern. Remarkably, the rotation of the BEC and the topological properties of the vortex lattice can be monitored nondestructively through the cavity output field.

DOI
10.1103/physrevresearch.7.013170

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Työväentutkimus Vuosikirja•Mar 1, 2006•0 citations
The appearance of quantized vortices in a superfluid and a Bose-Einstein condensate (BEC) stems from their nontrivial response to time-reversal symmetry (TRS). Here, we show that breaking of the TRS by, for example, rotation or an external synthetic magnetic field in a transversely driven BEC coupled to a single mode of an optical cavity modifies drastically Dicke superradiance and self-ordering phenomena in this system. In particular, photon scattering from the pump laser into the cavity is amplified by rotational motion of the BEC, leading to so-called “rotational superradiance”—in a loose analogy to black-hole physics—with distinct critical scaling properties. In turn, cavity photons mediate long-range, periodic attractive interactions among the vortices, which compete with pairwise logarithmic repulsive vortex interactions and deform the Abrikosov triangular vortex lattice favoring a stripe-like pattern. Remarkably, the rotation of the BEC and the topological properties of the vortex lattice can be monitored nondestructively through the cavity output field.
We report on the first experimental realization of the Dicke quantum phase transition realized in the quantum motion of a Bose–Einstein condensate coupled to an optical cavity. Conceptually, the transition is driven by cavity-mediated long-range interactions, giving rise to the emergence of a self-organized supersolid phase. The Dicke phase transition, predicted in 1973, has not been demonstrated experimentally before this work, both due to fundamental and technological reasons. These challenges have been overcome in the present thesis by employing atomic momentum states of a Bose-Einstein condensate, which are coupled via two-photon Raman transitions involving a cavity photon and a free-space pump photon. This open-system implementation of the Dicke model allows to tune all relevant parameters and offers a unique detection scheme to monitor the manybody system in real time. We demonstrate that the phase transition is accompanied by a macroscopically occupied cavity field and a striking change in the atomic momentum distribution, due to spontaneous self-organization of the atomic density on a checkerboard lattice. The boundary of the transition is mapped out by scanning two parameters of the Dicke model, to reveal a phase diagram in close agreement with the model description. Two different ordered configurations are allowed in the superradiant phase, giving rise to the concept of spontaneous symmetry breaking at the phase transition. We experimentally distinguish the symmetry-broken states and study the origin of the symmetry-breaking process. The finite spatial extension of our system induces a small symmetry-breaking field which changes randomly on each experimental realization. The influence of this field is studied and shown to diminish upon dynamically crossing the transition point with increasing transition rates.
We examine the superradiance of a Bose–Einstein condensate pumped with a Laguerre–Gaussian laser of high winding number, e.g., . The laser beam transfers its orbital angular momentum (OAM) to the condensate at once due to the collectivity of the superradiance. An ℓ -fold rotational symmetric structure emerges with the rotatory superradiance. ℓ number of single-charge vortices appear at the arms of this structure. Even though the pump and the condensate profiles initially have cylindrical symmetry, we observe that it is broken to ℓ -fold rotational symmetry at the superradiance. Breaking of the cylindrical symmetry into the ℓ -fold symmetry and OAM transfer to the condensate become significant after the same critical pump strength. Reorganization of the condensate resembles the ordering in the experiment by Esslinger and colleagues (2010 Nature 264 1301). We numerically verify that the critical point for the onset of the reorganization, as well as the properties of the emitted pulse, conform to the characteristics of superradiant quantum phase transition.
A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose-Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-ranged interactions between the condensed atoms. These are induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.
The supersolid phase characterized by the superfluid and long-range spatial periodicity of crystalline order is central to many branches of science ranging from condensed matter physics to ultracold atomic physics. Here we study a self-ordered checkerboard supersolid phase originating from dynamical spin-orbit coupling for a transversely pumped atomic Bose-Einstein condensate trapped in a ring cavity, corresponding to a superradiant anti-Tavis-Cummings phase transition. In particular, an undamped gapless Goldstone mode is observed in contrast to the experimentally realized lattice supersolid with a gapped roton mode for Dicke superradiance. This zero-energy mode reveals the rigidity of the self-ordered superradiant phase, which spontaneously breaks a continuous translational symmetry. Our work will highlight the significant opportunities for exploring long-lived supersolid matter by utilizing dynamical spin-orbit coupling in controllable optical cavities.
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
This thesis contains theoretical studies of weakly interacting, trapped Bose-Einstein condensed gases. The main emphasis is on the rotational properties of these systems. A typical Bose-Einstein condensate reacts to external rotation by forming singly quantized vortices. By the word ”typical” we refer to a condensate with repulsive interparticle interactions and with a frozen spin degree of freedom. However, there are some atomic species for which the low-energy interactions are attractive. Moreover, the tuning of different condensate properties is relatively easy. For example, there are ways to experimentally change the effective interaction from repulsive to attractive. For an attractively interacting condensate the vortex is not the only possible rotational state but the sample may also experience rotation through its center of mass. In the first part of the thesis, we analyze some properties of a rotating attractive Bose gas at the zero temperature limit. First, we note that in order to maintain energetical stability, the gas has to be rotated in an external trap which is steeper than a harmonic trap. We study the system in an anharmonic quadratic + quartic potential. The rotating ground state phase-space is determined with analytical and numerical methods. If the interactions are strong enough, the rotating ground state appears to be a state with the rotating center of mass. On the other hand, at the limit of weak interactions the system experiences rotation by forming a multiply quantized vortex. We also determine the spectrum of elementary excitations for these quantum many-particle states. We find that the broken symmetry of the center of mass rotating state induces an additional zero-energy (Goldstone) mode and that the small oscillations of the ground state exhibit the decoupling between the center of mass and relative motions. If the spin of the atoms is allowed to change freely, a rich variety of topological excitations in condensates can be studied. External rotation is one of the tools for examining the excitations in spinor condensates. In a spinless scalar condensate the appearance of a quantized vortex is manifested by the vortex line in which the condensate density vanishes. In the plane perpendicular to the vortex line, one speaks of the vortex core for the density minimum. We study the properties of slowly rotated F = 1 spinor condensates and show that for ferromagnetic interactions the ground state is a coreless vortex. While the individual spin components may carry ordinary vortices the overall density of the system is coreless. We also study a method to create a point-like monopole structure in a ferromagnetic condensate by suitably imprinting vortices and solitons for different spin components of the condensate.