Adiabatic transfer of light in a double cavity and the optical Landau-Zener problem

Miladinovic, N.; Hasan, Faiyaz; Chisholm, Nicholas; Linnington, I. E.; Hinds, E. A.; O’Dell, D. H. J.

doi:10.1103/physreva.84.043822

Cited by 13 publications

(28 citation statements)

References 64 publications

(165 reference statements)

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“…In Ref. [54] the lasing in the two-qubit system was demonstrated by solving numerically the Bloch-type equations (68). Besides demonstrating the population inversion between the operating levels, an additional signal with the frequency matching the distance between the operating levels was applied, to stimulate the transition from the upper operating level to the lower one.…”

Section: Lasing In the Two-qubit Systemmentioning

confidence: 99%

“…Then another signal stimulating transitions between the operating laser levels is applied f (t) = f ac sin ωt + f L sin ω L t with ω L = E 2 − E 1 . Solving the system of equations (68), one obtains the population of i-th level of our two-qubit system, P i = x ii . The results of the calculations are presented in Fig.…”

Section: Lasing In the Two-qubit Systemmentioning

confidence: 99%

“…Having the purpose of presenting and describing specific results for the multiphoton transitions, our consideration is limited to the Josephson-junction qubits. We note however that similar phenomena can be studied in different quantum objects, which can be described as two-or multi-level systems, such as quantum wires and dots [56][57][58][59][60], nitrogen vacancy centers in diamond [61,62], ultracold atoms [63][64][65], nanomechanical and optomechanical setups [66][67][68], electronic spin systems, two-dimensional electron gas, and graphene [69][70][71].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices.We present recent results for the driven superconducting qubit -resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing. Contents

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Section: Lasing In the Two-qubit Systemmentioning

confidence: 99%

Section: Lasing In the Two-qubit Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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“…This has led other authors [71], as well as us [72], to suggest that Landau-Zener type physics might be relevant to the optical dynamics caused by membrane motion. The celebrated Landau-Zener problem is one of the few exactly solvable problems in time-dependent quantum mechanics and provides a paradigm for analyzing the dynamical control of quantum systems, including the breakdown of adiabatic transfer between states.…”

Section: Introductionmentioning

confidence: 99%

“…Applying this to the electromagnetic field where photon number is not conserved is one of the main themes of this paper. In our previous paper [72] we showed how to approximately map the dynamics of two interacting classical optical fields obeying the Maxwell wave equation in the membrane-in-the-middle cavity system onto the mathematics of the Landau-Zener model, and hence how to analyze the efficiency of light transfer from one subcavity to the other by moving the membrane. Such deterministic transfer of light between cavities is a basic element of a quantum network [73], and has technological significance for cavity-QED realizations of quantum information processing [74].…”

Section: Introductionmentioning

confidence: 99%

Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

Hasan

O’Dell

2016

Phys. Rev. A

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We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane ("membrane-in-the-middle" set-up). Our approach is based on the Maxwell wave equation, and complements previous studies based on an effective Hamiltonian. The analysis shows that for slowly moving and weakly reflective membranes the dynamics can be approximated by unitary, first-order-in-time evolution given by an effective Schrödinger-like equation with a Hamiltonian that does not depend on the membrane speed. This approximate theory is the one typically adopted in cavity optomechanics and we develop a criterion for its validity. However, in more general situations the full second-order wave equation predicts light dynamics which do not conserve energy, giving rise to parametric amplification (or reduction) that is forbidden under first order dynamics and can be considered to be the classical counterpart of the dynamical Casimir effect. The case of a membrane moving at constant velocity can be mapped onto the Landau-Zener problem but with additional terms responsible for field amplification. Furthermore, the nature of the adiabatic regime is rather different from the ordinary Schrödinger case, since mode amplitudes need not be constant even when there are no transitions between them. The LandauZener problem for a field is therefore richer than in the standard single-particle case. We use the work-energy theorem applied to the radiation pressure on the membrane as a self-consistency check for our solutions of the wave equation and as a tool to gain an intuitive understanding of energy pumped into/out of the light field by the motion of the membrane.

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Dicke‐type phase transition in a multimode optomechanical system

2015

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We consider the "membrane in the middle" optomechanical model consisting of a laser pumped cavity which is divided in two by a flexible membrane that is partially transmissive to light and subject to radiation pressure. Steady state solutions at the mean-field level reveal that there is a critical strength of the light-membrane coupling above which there is a symmetry breaking bifurcation where the membrane spontaneously acquires a displacement either to the left or the right. This bifurcation bears many of the signatures of a second order phase transition and we compare and contrast it with that found in the Dicke model. In particular, by studying limiting cases and deriving dynamical critical exponents using the fidelity susceptibility method, we argue that the two models share very similar critical behaviour. For example, the obtained critical exponents indicate that they fall within the same universality class. Away from the critical regime we identify, however, some discrepancies between the two models. Our results are discussed in terms of experimentally relevant parameters and we evaluate the prospects for realizing Dicke-type physics in these systems.Comment: 14 pages, 6 figure

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Adiabatic transfer of light in a double cavity and the optical Landau-Zener problem

Cited by 13 publications

References 64 publications

Multiphoton transitions in Josephson-junction qubits (Review Article)

Multiphoton transitions in Josephson-junction qubits (Review Article)

Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field

Dicke‐type phase transition in a multimode optomechanical system

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