Optical Bistability with Small Numbers of Atoms

Sarkar, Sarben; Satchell, J.S.

doi:10.1209/0295-5075/3/7/005

Cited by 25 publications

(27 citation statements)

References 13 publications

(7 reference statements)

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“…The number of different r [ ] n n n , , 11 10 01 , i.e. the total number degrees of freedom of the system is The same scaling was independently observed in other publications: to our knowledge the first published mention of this scaling was reported by Sarkar and Satchell in 1987 [44], however without providing a concise explanation. In reference to their work, Carmichael provides an explanation of this scaling in his book based on an operator expectation value hierarchy expansion [38].…”

supporting

confidence: 75%

Efficient and exact numerical approach for many multi-level systems in open system CQED

Gegg

Richter

2016

New J. Phys.

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In this paper we generalize the numerically exact expansion scheme for many two-level systems coupled to a bosonic (cavity) mode under open system conditions to the case of multi-level systems. For the two-level systems the method is derived from physical and intuitive arguments and the efficient numerical modeling up to hundreds of two-level systems is described. We thereby perform an analysis that allows a natural generalization to multi-level systems. The focus of the paper lies on a comprehensible view on the underlying physics. This facilitates direct application of the method and the use of additional generalizations and approximations.

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supporting

confidence: 75%

Efficient and exact numerical approach for many multi-level systems in open system CQED

Gegg

Richter

2016

New J. Phys.

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“…4(a). There is striking agreement between the exact quantum results and the MF results; where MF theory predicts collective bistability, the Liouvillian gap decreases to Γ γ [57].…”

Section: Collective Bistability and Switchingmentioning

confidence: 52%

“…While this limit may seem unnatural for arrays of photonic cavities, it could be achieved using an external mirror, and it is in fact quite natural for other open quantum systems, such as ensembles of Rydberg atoms [64,66,81] or trapped ions [82,83]. We calculate the Liouvillian gap exactly by taking advantage of an efficient parameterization of the accessible space of density matrices (see [57,84] and Sec. C in the appendix); we show the Liouvillian gap for N = 20 as a function of µ/γ and Ω/γ in Fig.…”

Section: Collective Bistability and Switchingmentioning

confidence: 99%

Collective phases of strongly interacting cavity photons

Wilson

Mahmud

et al. 2016

Phys. Rev. A

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We study a coupled array of coherently driven photonic cavities, which maps onto a drivendissipative XY spin-1 2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.Despite numerous outstanding questions, the study of quantum many-body systems in thermal equilibrium is on relatively solid ground. In particular, very general guiding principles help to categorize the possible equilibrium phases of matter, and predict in what situations they can occur [1][2][3]. In comparison, quantum manybody systems that are far from equilibrium are less thoroughly understood, motivating a large scale effort to explore non-equilibrium dynamics experimentally, in particular using atoms, molecules, and photons [4][5][6][7][8][9]. At the same time, it has become clear that studying nonequilibrium physics in these systems is often more natural than studying equilibrium physics; they are, in general, intrinsically non-equilibrium. For example, thermal equilibrium is essentially never a reasonable assumption in photonic systems, where dissipation must be countered by active pumping [10]. Indeed, the inadequacy of equilibrium descriptions for photonic systems has long been recognized [11], even though close analogies to thermal systems sometimes exist [12][13][14][15][16].Until recently, photonic systems have been restricted to a weakly interacting regime. With notable progress towards generating strong optical nonlinearities at the few-photon level, for example with atoms coupled to small-mode-volume optical devices [17][18][19][20][21][22], Rydberg polaritons [23,24], and circuit-QED devices [25][26][27][28], this situation is rapidly changing. The production of strongly interacting, driven and dissipative gases of photons appears to be feasible [29,30], and affords exciting opportunities to explore the properties of open quantum systems in unique contexts, while studying the applicability of theoretical treatments designed with more weakly interacting systems in mind. For example, it is not fully understood how the steady states of these systems relate to the equilibrium states of their "closed" c...

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“…Techniques to represent and solve the master equation on this symmetrized Liouville space have been discussed for example in Refs. [48][49][50]. In the present case the Liouvillian is block diagonal with blocks of dimension ∼ N .…”

Section: Solution Of the Full Master Equationmentioning

confidence: 99%

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

et al. 2017

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Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the manybody dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.Time-reversal has fascinated and puzzled physicists for centuries. In an iconic example, Josef Loschmidt argued that the second law of thermodynamics would be violated by time-reversing an entropy-increasing collision [1]. Ludwig Boltzmann responded by formulating the probabilistic definition of entropy, one of the cornerstones of statistical mechanics, and, now a fundamental concept in quantum information. Since the days of Boltzmann and Loschmidt, the notion of time-reversal has moved from the arena of thought experiments into the laboratory, with time-reversal of non-interacting quantum systems in the form of Hahn spin echoes [2] forming an essential part of nuclear magnetic resonance (NMR) [3] and magnetic resonance imaging.Recently, the experimental implementation of manybody time-reversal protocols [4,5] in atomic quantum systems have attracted attention [6][7][8][9] for their potential to quantify the flow of quantum information in time and set bounds on thermalization times [10][11][12][13], which might also enable experimental tests of the holographic duality between quantum and gravitational systems [6,[14][15][16][17]. The key quantities sought after are special types of outof-time-order correlation (OTOC) functions,whereŴ (τ ) = e iĤτŴ e −iĤτ , withĤ an interacting many-body Hamiltonian andŴ andV two commuting unitary operators. Physically, F (τ ) measures the "scrambling" of quantum information across the system's manybody degrees of freedom, for example, how fast an initial * These authors contributed equally.† john.bollinger@nist.gov ‡ arey@jila.colorado.edu local perturbation becomes inaccessible to local probesencapsulates the degree by which the initially commuting operatorsŴ andV fail to commute at later times due to the interactions generated byĤ, which we adopt as an operational definition of scrambling.Most theoretical studies of scrambling have focused on so-called fast scramblers in thermal states [10,11,16]...

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Optical Bistability with Small Numbers of Atoms

Cited by 25 publications

References 13 publications

Efficient and exact numerical approach for many multi-level systems in open system CQED

Efficient and exact numerical approach for many multi-level systems in open system CQED

Collective phases of strongly interacting cavity photons

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

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