Analytical analysis of the “collapse-revival” effect in the Jaynes–Cummings model

Феранчук, И. Д.; Leonov, A. V.

doi:10.1016/j.physleta.2008.12.006

Cited by 15 publications

(15 citation statements)

References 18 publications

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“…This effect was predicted theoretically [17] and later observed experimentally [18]. Its qualitative explanation and analytical description was also given by [19][20][21]. It was shown that the evolution of the population of the atomic states is characterized by two time scales.…”

Section: Introductionmentioning

confidence: 64%

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Collapse-and-revival dynamics of strongly laser-driven electrons

2013

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The relativistic quantum dynamics of an electron in an intense single-mode quantized electromagnetic field is investigated with special emphasis on the spin degree of freedom. In addition to fast spin oscillations at the laser frequency, a second time scale is identified due to the intensity dependent emissions and absorptions of field quanta. In analogy to the well-known phenomenon in atoms at moderate laser intensity, we put forward the conditions of collapses and revivals for the spin evolution in laser-driven electrons starting at feasible 10 18 W/cm 2 .PACS number(s): 12.20.-m, 13.88.+e

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Section: Introductionmentioning

confidence: 64%

“…This gives the possibility of changing the summation over n to an integration over the complex variable. Then this integral in the complex plane can be evaluated using the same approach as in [19]. This approach is based on the saddle point method [27].…”

Section: Electron Spin Dynamics In a Single-mode Quantized Fieldmentioning

confidence: 99%

Collapse-and-revival dynamics of strongly laser-driven electrons

2013

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“…The Rabi oscillations of a two-level atom in a resonant, single-mode coherent field state is one of the simplest phenomena in quantum optics. Nevertheless, it exhibits surprisingly complex features at the mesoscopic scale (few tens of photons) [1][2][3][4]. The oscillations, at an angular frequency Ω 0 √ n, collapse and revive (n is the average photon number in the coherent state; Ω 0 is the vacuum Rabi frequency measuring the atom-field coupling).…”

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confidence: 99%

“…The cavity C, cooled down to 1.5 K by a wet 4 He cryostat, sustains a linearly polarized Gaussian standingwave mode with a waist w = 6 mm [3]. Its damping time is T Cav = 8.1 ± 0.3 ms. Its temperature corresponds to an average thermal photon number n th = 0.38.…”

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confidence: 99%

Quantum Rabi Oscillations in Coherent and in Mesoscopic Cat Field States

et al. 2019

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The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of 'cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of non-classical states in cavity and circuit Quantum Electrodynamics. PACS numbers:The Rabi oscillations of a two-level atom in a resonant, single-mode coherent field state is one of the simplest phenomena in quantum optics. Nevertheless, it exhibits surprisingly complex features at the mesoscopic scale (few tens of photons) [1][2][3][4]. The oscillations, at an angular frequency Ω 0 √ n, collapse and revive (n is the average photon number in the coherent state; Ω 0 is the vacuum Rabi frequency measuring the atom-field coupling). The collapse, occurring on a time scale T c = 2 √ 2/Ω 0 , results from the quantum field amplitude uncertainty and from the corresponding dephasing of the Rabi oscillations. The (first) revival, around T r = 4π √ n/Ω 0 , results from the rephasing of oscillations associated to different photon numbers [5]. This revival provides a landmark illustration of field amplitude quantization [6]. Between collapse and revival, the field evolves into an entangled atom-field state, involving two coherent states with different phases [7,11,[35][36][37]. It is called a "cat state" in memory of Schrödinger's metaphor. Close to t = T r /2, the atomic state factors out of a field "cat", superposition of coherent states with opposite phases [5].These phenomena can be observed in systems implementing the Jaynes and Cummings model, a spin-1/2 coupled to a one-dimensional harmonic oscillator [12]. Ions in traps [13,14], cavity quantum electrodynamics (CQED) [3,6] and circuit quantum electrodynamics (cQED) [16, 39] are thus ideal platforms for this observation.Nevertheless, revival observations have so far been limited to small photon numbers since experiments face formidable challenges. For microwave CQED with superconducting cavities crossed by fast Rydberg atoms, the interaction time is limited to a few vacuum Rabi periods, 2π/Ω 0 . Revivals have been observed only for n 1 [6,17]. Early revivals induced by a time-reversal of the collapse can be observed for larger n values (about 10), but the maximum separation of the cat compo-nents is small [18,19]. Ion traps have similar limitations [13,20]. In cQED, the limited coherence time of tunable superconducting qubits makes it difficult to observe long-term dynamics in the resonant regime [21]. Large cat-state preparation so far relie...

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“…It is noteworthy that analogous quasiintersections, higher order resonances (u k ≈ k/f), will arise according to the structure of the accurate solution of the JCM [8,9] as the field amplitude is increased further. However, an analysis of the temporal problem with arbitrary field amplitudes even within the framework of the literature approach [12] is fraught with rather tedious numerical calculations and will be reported separately. We will limit ourselves within the scope of the present work to an analytical investigation based on Eq.…”

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Resonant retuning of Rabi oscillations in a two-level system

Leonov

Феранчук

2009

J Appl Spectrosc

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The evolution of a two-level system in a single-mode quantum field is considered beyond the rotating wave approximation. The existence of quasi-degenerate energy levels is shown to influence the essential characteristics of temporal and amplitude Rabi oscillations of the system in a resonant manner.Introduction. The Jaynes-Cummings model (JCM) is currently undergoing a second birth due to its use to describe the interaction of the elementary quantum cell (two-level atom) with a quantum electromagnetic field in a cavity [2]. The actual physical manifestation of such a structure can be varied (resonant transitions in atoms, quantum dots, impurity centers, etc.). However, the use of the JCM in any instance enables its qualitative features to be described. The applied significance of the JCM in spectroscopy and quantum optics is due to the ability to describe based on it the population change dynamics of quantum system states upon the reception, retention, and transfer of information [3,4].The most common approaches to a theoretical study of the evolution of the JCM are based on the rotating wave approximation (RWA) and Bloch equations in which the quantum field is replaced by a classical one. A characteristic system property in this instance is the so-called Rabi oscillations, periodic changes with time of the population of atomic states [5]. Analogous oscillations were recently observed also for the population as a function of the field amplitude, Rabi amplitude oscillations (RAO). This has applied significance for controlling the quantum system [6 and references therein].It was recently shown [7] that consideration of the non-Markovian nature of the evolution of the two-level atom in an external periodic field leads to damping of RAO. The energy dissipation process in the cavity as an open system was viewed as the physical reason for the change of RAO. Herein it is demonstrated that population amplitude oscillations can behave analogously due to another physical effect that is essentially quantum in nature. It is due to quasi-interchange of JCM energy levels that arise on exceeding the limits of the RWA [8,9] and is resonant in nature with respect to the amplitude field. An analysis of the relationship between these effects under actual experimental conditions is important for understanding the role of anti-rotational terms in the JCM Hamiltonian and a correct description of the system evolution.Quasi-Interchange of JCM Energy Levels. Let us examine the JCM Hamiltonian

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Analytical analysis of the “collapse-revival” effect in the Jaynes–Cummings model

Cited by 15 publications

References 18 publications

Collapse-and-revival dynamics of strongly laser-driven electrons

Collapse-and-revival dynamics of strongly laser-driven electrons

Quantum Rabi Oscillations in Coherent and in Mesoscopic Cat Field States

Resonant retuning of Rabi oscillations in a two-level system

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