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arXiv:1606.06058 · Physical Review Letters

Fragmented Superradiance of a Bose-Einstein Condensate in an Optical Cavity

Axel U. J. Lode, Christoph Bruder

Published Jan 6, 2017• 83 citations
arXivHTMLPDF

Abstract

The Dicke model and the superradiance of two-level systems in a radiation field have many applications. Recently, a Dicke quantum phase transition has been realized with a Bose-Einstein condensate in a cavity. We numerically solve the many-body Schrödinger equation and study correlations in the ground state of interacting bosons in a cavity as a function of the strength of a driving laser. Beyond a critical strength, the bosons occupy multiple modes macroscopically while remaining superradiant. This fragmented superradiance can be detected by analyzing the variance of single-shot measurements.

DOI
10.1103/physrevlett.118.013603

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The Dicke model and the superradiance of two-level systems in a radiation field have many applications. Recently, a Dicke quantum phase transition has been realized with a Bose-Einstein condensate in a cavity. We numerically solve the many-body Schrödinger equation and study correlations in the ground state of interacting bosons in a cavity as a function of the strength of a driving laser. Beyond a critical strength, the bosons occupy multiple modes macroscopically while remaining superradiant. This fragmented superradiance can be detected by analyzing the variance of single-shot measurements.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
We consider laser-pumped one-dimensional two-component bosons in a parabolic trap embedded in a high-finesse optical cavity. Above a threshold pump power, the photons that populate the cavity modify the effective atom trap and mediate a coupling between the two components of the Bose–Einstein condensate. We calculate the ground state of the laser-pumped system and find different stages of self-organization depending on the power of the laser. The modified potential and the laser-mediated coupling between the atomic components give rise to rich many-body physics: an increase of the pump power triggers a self-organization of the atoms while an even larger pump power causes correlations between the self-organized atoms—the BEC becomes fragmented and the reduced density matrix acquires multiple macroscopic eigenvalues. In this fragmented superradiant state, the atoms can no longer be described as two-level systems and the mapping of the system to the Dicke model breaks down.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.
We analytically investigate the ground-state properties of two-component Bose-Einstein condensates with few ⁸⁷Rb atoms inside a high-quality cavity quantum electrodynamics. In the SU(2) representation for atom, this quantum system can be realized a generalized Dicke model with a quadratic term arising from the interatomic interactions, which can be controlled experimentally by Feshbach resonance technique. Moreover, this weak interspecies interaction can give rise to an important zero-temperature quantum phase transition from the normal to the superradiant phases, where the atomic ensemble in the normal phase is collectively unexcited while is macroscopically excited with coherent radiations in the superradiant phase. Finally, we propose to observe this predicted quantum phase transition by measuring the direct and striking signatures of the photon field in terms of a heterodyne detector out of the cavity.
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.