Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment

Cohn, Jeffrey; Safavi-Naini, Arghavan; Lewis-Swan, Robert J.; Bohnet, Justin; Gärttner, Martin; Gilmore, Kevin; Jordan, J. E.; Rey, Ana María; Bollinger, John J.; Freericks, J. K.

doi:10.1088/1367-2630/aac3fa

Cited by 48 publications

(45 citation statements)

References 21 publications

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“…It has been employed, for instance, in studies of ground-state and excited-state quantum phase tran-sitions [33,[40][41][42][43][44], entanglement creation [45], nonequilibrium dynamics [46][47][48][49], quantum chaos [50][51][52][53], and monodromy [54,55]. Recently, the model has received revived attention due to new experiments with ion traps [56,57] and the analysis of the OTOC [58,59].In the classical limit, the Dicke model presents regular and chaotic regions depending on the Hamiltonian parameters and excitation energies [53]. This allows us to benchmark the OTOC growth against the presence and absence of chaos.…”

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confidence: 99%

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

et al. 2019

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The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.Quantum chaos tries to bridge quantum and classical mechanics. The search for quantum signatures of classical chaos has ranged from level statistics [1,2] and the structure of the eigenstates [3,4] to the exponential increase of complexity [5,6] and the exponential decay of the overlap of two wave packets [7][8][9][10]. Recently, the pursuit of exponential instabilities in the quantum domain has been revived by the conjecture of a bound on the rate growth of the out-of-time-ordered correlator (OTOC) [11,12]. First introduced in the context of superconductivity [13], the OTOC is now presented as a measure of quantum chaos, with its growth rate being associated with the classical Lyapunov exponent. The OTOC is not only a theoretical quantity, but has also been measured experimentally via nuclear magnetic resonance techniques [14][15][16][17].The correspondence between the OTOC growth rate and the classical Lyapunov exponent has been explicitly shown in two cases of one-body chaotic systems, the kicked-rotor [18] and, after a first unsuccessful attempt [19], the stadium billiard [20]. It was also achieved for chaotic maps [21]. For interacting many-body systems, while exponential behaviors for the OTOC have been found for the Sachdev-Ye-Kitaev model [11,22] and for the Bose-Hubbard model [23,24], a direct demonstration of the quantum-classical correspondence has not yet been made. Studies in this direction include [6,[25][26][27][28][29] and [30].Here, we investigate the OTOC for the Dicke model [31,32]. Comparing with one-body systems, the model is a step up toward an explicit quantum-classical correspondence for interacting many-body systems, since it contains N atoms interacting with a quantized field.The Dicke model was originally proposed to explain the collective phenomenon of superradiance: the field mediates interatomic interactions, which causes the atoms to act collectively [31,33]. Superradiance has been experimentally studied with ultracold atoms in optical cavities [34][35][36][37][38][39]. The model has also found applications beyond superradiance in various different fields. It has been employed, for instance, in studies of ground-state and excited-state quantum phase tran-sitions [33,[40][41][42][43][44], entanglement creation [45], nonequilibrium dynamic...

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confidence: 99%

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

et al. 2019

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“…1D), the signal is just the OTOC S ϕ = I z (t)Φ(t)I z (t)Φ β=0 . We can further evaluate the OTO commutator [25,[32][33][34] C zz = |[I z , I z (t)]| 2 β=0 , by repeating the experiment varying ϕ in integer steps, ϕ n = 2πn/Q, n = 1, ..., Q and extracting its discrete Fourier transform [20], S δ q (t) = Q n=1 e iqϕ S δ ϕn (t). The MQC intensities S q represent the contribution of all coherences of order q in the density matrix of the multispin state, where a coherence q with respect to a given basis (here the Zeeman basis |m z ) is any element r|ρ|s with s − r = q.…”

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confidence: 99%

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

et al. 2020

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Evaluating the role of perturbations versus the intrinsic coherent dynamics in driving to equilibrium is of fundamental interest to understand quantum many-body thermalization, in the quest to build ever complex quantum devices. Here we introduce a protocol that scales down the coupling strength in a quantum simulator based on a solid-state nuclear spin system, leading to a longer decay time T2, while keeping perturbations associated to control error constant. We can monitor quantum information scrambling by measuring two powerful metrics, out-of-time-ordered correlators (OTOCs) and Loschmidt Echoes (LEs). While OTOCs reveal quantum information scrambling involving hundreds of spins, the LE decay quantifies, via the time scale T3, how well the scrambled information can be recovered through time reversal. We find that when the interactions dominate the perturbation, the LE decay rate only depends on the interactions themselves, T3 ∝ T2, and not on the perturbation. Then, in an unbounded many-spin system, decoherence can achieve a perturbation-independent regime, with a rate only related to the local second moment of the Hamiltonian.

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“…In the interaction picture with respect to the phonon modes and keeping only near‐resonant terms we then obtain

H_{normalΩ} ≃ \sum_{i} \frac{g}{2} [σ_{i}^{+} (() a {prefixe}^{i {normalΔ}_{x, b} t} + a^{†} {prefixe}^{- i {normalΔ}_{x, r} t}) + normalH . normalc .]

where we identified

a \equiv b_{x, COM}

and

g \equiv η_{normalCOM}^{x} ξ_{normalCOM}^{x} {normalΩ}_{x}

. We now define

\begin{matrix} true \\ left ω_{c} = 0true \frac{1}{2} ({normalΔ}_{x, b} + {normalΔ}_{x, r}), \\ left ω_{0} = 0true \frac{1}{2} ({normalΔ}_{x, b} - {normalΔ}_{x, r}) \end{matrix}

and after eliminating the time‐dependence via the unitary transformation

U false(t false) = {prefixe}^{- i (ω_{c} a^{†} a + ω_{0} S_{z}) t}

we obtain the effective Hamiltonian

\begin{matrix} true \\ right H_{eff}^{false(x false)} ≃ ω_{c} a^{†} a + ω_{0} S_{z} + g (a + a^{†}) S_{x} \end{matrix}

This and closely related schemes have already been discussed in many previous works for implementing effective Rabi‐ and Dicke models,...…”

Section: Effective Cavity Qed Models With Trapped Ionsmentioning

confidence: 99%

“…In this work we investigate the use of systems of trapped ions as a quantum simulator for multi‐dipole cavity QED systems in the USC regime. This platform is naturally suited for this purpose since experimental techniques for implementing Jaynes–Cummings‐, Rabi‐ and Dicke‐type couplings between the internal atomic states and motional modes (which represent the photons in the effective model) are already well established . However, for

N > 1

such models provide very restricted or inconsistent descriptions of quantum electrodynamics beyond the weak‐coupling regime and must be complemented by additional interaction terms .…”

Section: Introductionmentioning

confidence: 99%

Quantum Simulation of Non‐Perturbative Cavity QED with Trapped Ions

2020

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The simulation of non-perturbative cavity-QED effects is discussed using systems of trapped ions. Specifically, the implementation of extended Dicke models with both collective dipole-field and direct dipole-dipole interactions is addressed, which represent a minimal set of models for describing light-matter interactions in the ultrastrong and deep-strong coupling regime. It is shown that this approach can be used in state-of-the-art trapped ion setups to investigate excitation spectra or the transition between sub-and superradiant ground states, which are currently not accessible in any other physical system. The analysis also reveals the intrinsic difficulty of accessing this non-perturbative regime with larger numbers of dipoles, which makes the simulation of many-dipole cavity QED a particularly challenging test case for future quantum simulation platforms.

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Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment

Cited by 48 publications

References 21 publications

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System

Quantum Simulation of Non‐Perturbative Cavity QED with Trapped Ions

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