Erratum: Realization of the Dicke Model Using Cavity-Assisted Raman Transitions [Phys. Rev. Lett. 
<b>113</b>
, 020408 (2014)]

Baden, M. P.; Arnold, K. J.; Grimsmo, Arne L.; Parkins, Scott; Barrett, M. D.

doi:10.1103/physrevlett.118.199901

Cited by 44 publications

(66 citation statements)

References 2 publications

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“…This model is relevant to cavity QED systems based on cold atoms [53][54][55][56] and circuit QED systems based on superconducting qubits [57][58][59][60][61][62][63]. As schematically illustrated in Fig.…”

Section: Fig 1: (Color Online)mentioning

confidence: 99%

“…In particular, if the atoms are initialized (by, e.g., optical pumping) to be a fully spin-polarized state like |⇓ ≡ N j=1 |↓ , which is the case in real experiments [53,56], we have Ĵ 2 = N 2 ( N 2 + 1). At the mean-field level, we approximate âĴ µ as â Ĵ µ , which has an order of magnitude O(N 3 2 ) while the quantum fluctuation is expected to be no more than O(N ).…”

Section: Heisenberg Equation Of Motion and Its Semiclassical Reductionmentioning

confidence: 99%

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Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

2018

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Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.Introduction.-Phases and phase transitions of matter are key concepts for understanding complex many-body physics [1,2]. Recent experimental developments in various quantum simulators, such as ultracold atoms [3,4], trapped ions [5,6] and superconducting qubits [7,8], motivate us to seek for quantum many-body systems out of equilibrium [9][10][11], such as many-body localized phases [12][13][14][15][16][17] and Floquet topological phases [18][19][20][21][22][23][24][25].In recent years, much effort has been devoted to periodically driven (Floquet) quantum many-body systems that break the discrete time-translation symmetry (TTS) [26]. In contrast to the continuous TTS breaking [27][28][29] that has turned out to be impossible at thermal equilibrium [30,31], the discrete TTS breaking has been theoretically proposed [32][33][34][35][36] and experimentally demonstrated [37,38]. Phases with broken discrete TTS feature discrete time-crystalline (DTC) order characterized by periodic oscillations of physical observables with period nT , where T is the Floquet period and n = 2, 3, · · · . The DTC order is expected to be stabilized by many-body interactions against variations of driving parameters. Note that the system is assumed to be in a localized phase [33,34,36,37] or to have long-range interactions [38][39][40]. Otherwise, the DTC order only exists in a prethermalized regime [41,42] since the system will eventually be heated to a featureless infinite-temperature state due to persistent driving [43][44][45].While remarkable progresses are being made concerning the DTC phase, most studies focus on isolated systems. Indeed, as has been experimentally observed [37,38] and theoretically investigated [46], the DTC order in an open system is usually destroyed by decoherence. On the other hand, it is known that dissipation and decoherence can also serve as resources for quantum tasks such as quantum computation [47] and metrology [48]. From this perspective, it is natural to ask whether the DTC order exists and can even be stabilized in open systems [49]. Such a possibility has actually been pointed out in Ref. [41], but neither a detailed theoretical model nor a concrete experimental imp...

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Section: Fig 1: (Color Online)mentioning

confidence: 99%

Section: Heisenberg Equation Of Motion and Its Semiclassical Reductionmentioning

confidence: 99%

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

2018

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“…To this end, a quantum degenerate bosonic gas was placed into a high-finesse optical cavity subjected to a transverse off-resonant pump beam. Above a critical pump strength, the feedback between the atomic density distribution and the cavity field leads to a spontaneous formation of a symmetry broken phase in which the atoms form a checkerboard density pattern off which pump light is super-radiantly scattered into the cavity [6,[10][11][12][13][14][15][16]. Details of the steady-state diagram as for example different super-radiant fixed points [17,18], dynamic correlations [19], the damping of quasi-particles [20], self-ordered limit cycles [21], or prethermalization effects [22] have been investigated theoretically.…”

Section: Introductionmentioning

confidence: 99%

Cavity-induced chiral states of fermionic quantum gases

2016

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We investigate ultra-cold fermions placed into an optical cavity and subjected to optical lattices which confine the atoms to ladder structures. A transverse running-wave laser beam induces together with the dynamical cavity field a two-photon Raman-assisted tunneling process with spatially dependent phase imprint along the rungs of the ladders. We identify the steady states which can occur by the feedback mechanism between the cavity field and the atoms. We find the spontaneous emergence of a finite cavity field amplitude which leads to an artificial magnetic field felt by the fermionic atoms. These form a chiral insulating or chiral liquid state carrying a chiral current. We explore the rich state diagram as a function of the power of the transverse laser beam, the atomic filling, and the phase imprint during the cavity-induced tunneling. Both a sudden onset or a slow exponential activation with the transverse laser power of the self-organized chiral states can occur.

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“…Tunable open Rabi-Hubbard model.-Recently, several proposals to engineer effective light-matter interactions by suitable designed driving schemes have appeared [40][41][42][43], based on a variety of platforms including superconducting circuit QED, impurities in diamond, and ultracold atoms [4]. Here for concreteness we consider a lattice of coupled cavity-QED systems, where on each lattice site n there is a four-level system which is driven and coupled to a cavity mode (see Fig.…”

mentioning

confidence: 99%

“…Introduction.-A number of recent experimental breakthroughs [1][2][3][4] have spurred the investigation of nonequilibrium properties of hybrid quantum many-body systems of interacting matter and light. Characterized by excitations with a finite lifetime, when sustained by finiteamplitude optical drives they display steady-state phases that are generally far richer [5][6][7][8][9][10] than their equilibrium counterparts [11,12].…”

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confidence: 99%

Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model

et al. 2016

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We explore the phase diagram of the dissipative Rabi-Hubbard model, as could be realized by a Ramanpumping scheme applied to a coupled cavity array. There exist various exotic attractors, including ferroelectric, antiferroelectric, and incommensurate fixed points, as well as regions of persistent oscillations. Many of these features can be understood analytically by truncating to the two lowest lying states of the Rabi model on each site. We also show that these features survive beyond mean field, using matrix product operator simulations. DOI: 10.1103/PhysRevLett.116.143603 Introduction.-A number of recent experimental breakthroughs [1][2][3][4] have spurred the investigation of nonequilibrium properties of hybrid quantum many-body systems of interacting matter and light. Characterized by excitations with a finite lifetime, when sustained by finiteamplitude optical drives they display steady-state phases that are generally far richer [5][6][7][8][9][10] than their equilibrium counterparts [11,12]. Critical phenomena in these open driven-dissipative systems often come with genuinely new properties and novel dynamic universality classes, even when an effective temperature can be identified [13][14][15][16][17], a statement that can be made robust in renormalization group calculations [18,19]. Coupled cavity QED systems [20][21][22] have emerged as natural platforms to study many-body physics of open quantum systems. The current fabrication and control capabilities in solid-state quantum optics allows us to probe lattice systems [23][24][25][26][27][28][29][30][31] in the mesoscopic regime, providing a first glimpse into how macroscopic quantum behavior may arise far from equilibrium. It is therefore of interest to identify a physical system where a nonequilibrium phase transition (i) can be studied-at least in principle-in the thermodynamic limit, (ii) can be compared to an equilibrium analogue through a proper limiting procedure, and (iii) can be easily realized in an architecture that is currently available.The Rabi-Hubbard (RH) model [32] represents the minimal description of coupled cavity QED systems, explicitly containing terms which do not conserve the particle number. These terms are relevant for the lowfrequency behavior of the coupled system and their inclusion lead, in equilibrium, to a Z 2 -symmetry breaking phase transition between a quantum disordered paraelectric phase and an Ising ferroelectric [32,33]. The equilibrium RH transition requires a sizable intercavity hopping or light-matter interaction, of the order of the transition

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Erratum: Realization of the Dicke Model Using Cavity-Assisted Raman Transitions [Phys. Rev. Lett. 113 , 020408 (2014)]

Abstract: This corrects the article DOI: 10.1103/PhysRevLett.113.020408.

Cited by 44 publications

References 2 publications

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

Discrete Time-Crystalline Order in Cavity and Circuit QED Systems

Cavity-induced chiral states of fermionic quantum gases

Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model

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