Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation

Zueco, David; Reuther, Georg M.; Kohler, Sigmund; Hänggi, Peter

doi:10.1103/physreva.80.033846

Cited by 191 publications

(220 citation statements)

References 44 publications

(56 reference statements)

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“…Indeed, there have been a number of theoretical studies of this system, analyzing some of its rich static and dynamical properties (see, e.g., [19][20][21]). Also, the ultrastrong coupling between a superconducting flux qubit and a coplanar waveguide [22] or an LC resonator [23] has recently been demonstrated in experiments.…”

Section: Superconducting Circuits As Artificial Atomsmentioning

confidence: 99%

Atomic physics and quantum optics using superconducting circuits

You

Nori

2011

Nature

1,239

1,081

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Superconducting circuits based on Josephson junctions exhibit macroscopic quantum coherence and can behave like artificial atoms. Recent technological advances have made it possible to implement atomic-physics and quantum-optics experiments on a chip using these artificial atoms. This review presents a brief overview of the progress achieved so far in this rapidly advancing field. We not only discuss phenomena analogous to those in atomic physics and quantum optics with natural atoms, but also highlight those not occurring in natural atoms. In addition, we summarize several prospective directions in this emerging interdisciplinary field.Superconducting circuits with Josephson junctions can behave as artificial atoms. In these quantum circuits, the Josephson junctions act as nonlinear circuit elements (see Box 1). Such nonlinearity in a circuit ensures an unequal spacing between energy levels, so that the lowest levels can be individually addressed by using external fields (see, e.g., [1][2][3][4][5][6][7][8][9]). Experimentally, these circuits are fabricated on a micrometer scale and operated at mK temperatures. Because of the reduced dimensionality and thanks to the superconductivity, the environmentinduced dissipation and noise are greatly suppressed, so the circuits can behave quantum mechanically.Superconducting circuits based on Josephson junctions have recently become subjects of intense research because they can be used as qubits-controllable quantum two-level system-for quantum computing (see, e.g., [1-4] for reviews). Even though the typical decoherence times of these circuits fall short of the requirements for quantum computation, their macroscopic quantum coherence is sufficient for them to exhibit striking quantum behaviors. These circuits can have a number of superconducting eigenstates with discrete eigenvalues lower than the energy levels of the quasi-particle excitations that involve breaking Cooper pairs. This property allows these circuits to behave like superconducting artificial atoms. Indeed, there is a deep analogy between natural atoms and the artificial atoms made from superconducting circuits (see Box 2). Both have discrete energy levels and can exhibit coherent quantum oscillations between these levels. Whereas natural atoms may be controlled using visible or microwave photons that excite electrons from one state to another, the artificial atoms in the circuits are driven by currents, voltages and microwave photons that excite the system from one macroscopic quantum state to another.Differences between superconducting circuits and natural atoms include the different energy scales in the two systems, and how strongly each system couples to its environment; the coupling is weak for atoms and strong for circuits. In contrast to naturally occurring atoms, artificial atoms can be designed with specific characteristics and fabricated on a chip using standard lithographical technologies. With a view to applications, this degree of tunability is an important advantage over natural atoms. Thus, ...

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Section: Superconducting Circuits As Artificial Atomsmentioning

confidence: 99%

Atomic physics and quantum optics using superconducting circuits

You

Nori

2011

Nature

1,239

1,081

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“…It should be noted that below we consider the large detuning between the qubit and the NAMR, i.e., (ω 0 − ω) is several times larger (but not much larger) than the coupling constant g; thus, the rotating wave approximation can be applied. The effect of the counter-rotating terms on the results can also calculated in the large detuning case [55]. However, here we have neglected this effect because it only produces a small frequency shift and two-photon processes.…”

Section: Qubit-induced Phonon-phonon Interactionmentioning

confidence: 99%

Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators

et al. 2010

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The observation of quantized nanomechanical oscillations by detecting femtometer-scale displacements is a significant challenge for experimentalists. We propose that phonon blockade can serve as a signature of quantum behavior in nanomechanical resonators. In analogy to photon blockade and Coulomb blockade for electrons, the main idea for phonon blockade is that the second phonon cannot be excited when there is one phonon in the nonlinear oscillator. To realize phonon blockade, a superconducting quantum two-level system is coupled to the nanomechanical resonator and is used to induce the phonon self-interaction. Using Monte Carlo simulations, the dynamics of the induced nonlinear oscillator is studied via the Cahill-Glauber s-parametrized quasiprobability distributions. We show how the oscillation of the resonator can occur in the quantum regime and demonstrate how the phonon blockade can be observed with currently accessible experimental parameters.

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“…However, in the circuit quantum electrodynamic (QED), the artificial atoms may interact very strongly with on-chip resonant circuits [6][7][8][9][10], the RWA can not describe well the strong coupling regime [6]. Therefore, the JC model without the RWA is the focus of current interests [11][12][13][14][15][16][17][18][19][20][21].…”

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Exact solutions to the Jaynes-Cummings model without the rotating-wave approximation

Chen

Liu

Zhang

et al. 2011

EPL

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By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation can give all eigenvalues and eigenfunctions of this model with all values of the coupling strength and the detuning exactly, which can be readily applied to recent circuit quantum electrodynamic systems operating in the ultra-strong coupling regime.PACS numbers: 42.50. Pq, 03.65.Ge, 85.25.Cp, 03.67.Lx The Jaynes-Cummings (JC) model[1] describes the interaction of a two-level atom (qubit) with a single bosonic mode. It is a fundamental one in quantum optics. Based on the assumption of nearresonance and relatively weak atom-cavity coupling, the rotating-wave approximation (RWA) is usually employed, and analytically exact solution can be trivially obtained.Recently, the JC model is closely related to condensed matter physics. It can be realized in some solid-state systems recently, such as one Josephson charge qubit coupling to an electromagnetic resonator [2], the superconducting quantum interference device coupled with a nanomechanical resonator [3,4], and the most recently LC resonator magnetically coupled to a superconducting qubit [5][6][7]. In traditional quantum optics where the coupling between the two-level "natural" atom and the single bosonic mode is quite weak, RWA is the most useful approximation. However, in the circuit quantum electrodynamic (QED), the artificial atoms may interact very strongly with on-chip resonant circuits [6][7][8][9][10], the RWA can not describe well the strong coupling regime [6]. Therefore, the JC model without the RWA is the focus of current interests [11][12][13][14][15][16][17][18][19][20][21].However, due to the inclusion of the counter-rotating terms, the Bosonic number is not conserved, the Bosonic Fock space has infinite dimensions, so any solution without the RWA is highly nontrivial. In the recent years, several non-RWA approaches have been proposed in the Dicke model [12], the quantum Zeno effect [22], and the spin-boson model [23]. Especially, by using extended bosonic coherent states, the present authors have solved the Dicke model without the RWA exactly in the numerical sense [12]. The most simple N = 1 Dicke model is just the JC model. This numerically exact solutions to the JC model are also described in detail in Refs. [18,19]. To the best of our knowledge, an analytical exact solutions are still lacking in the literature to date.In this paper, we propose a new method to solve exactly the JC model without the RWA by means of extended bosonic coherent states. The correlations among bosons are added step by step until further corrections will not change the results. Different from our previous work where the pure coherent state are fixed, the eigenvalue α of the pure coherent state in this paper is tunable. By solving Schr Without the RWA, the Hamiltonian of a qubit interacting with a single bosonic mode reads ( = 1)where a ...

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Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation

Cited by 191 publications

References 44 publications

Atomic physics and quantum optics using superconducting circuits

Atomic physics and quantum optics using superconducting circuits

Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators

Exact solutions to the Jaynes-Cummings model without the rotating-wave approximation

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