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arXiv:quant-ph/0602219 · Physical Review B

Analogue of cavity quantum electrodynamics for coupling between spin and a nanomechanical resonator: Dynamic squeezing and coherent manipulations

Fei Xue, L. Zhong, Yong Li, C. P. Sun

Published Jan 11, 2007• 32 citations
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Abstract

In the cavity QED analogue for the coupling system of a spin and a nanomechanical resonator, we show that, when the nanomechanical resonator is quantized, a spin-boson model for this coupling system can refer to a Jaynes-Cummings (JC) or an anti-JC model. These observations predict some quantum optical phenomena, such as dynamic squeezing in the single oscillation mode of the nanomechanical resonator. By modulating the phase of rf magnetic field, one can switch the system between the JC and anti-JC model for the detection of the single spin.

DOI
10.1103/physrevb.75.033407

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In the cavity QED analogue for the coupling system of a spin and a nanomechanical resonator, we show that, when the nanomechanical resonator is quantized, a spin-boson model for this coupling system can refer to a Jaynes-Cummings (JC) or an anti-JC model. These observations predict some quantum optical phenomena, such as dynamic squeezing in the single oscillation mode of the nanomechanical resonator. By modulating the phase of rf magnetic field, one can switch the system between the JC and anti-JC model for the detection of the single spin.
We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generalized situations where the superconducting Josephson junction system is a multi-level system. We also address the practical issues concerning experimental realization.
We study interaction between a pair of indistinguishable two-level atoms and the single-mode cavity field. It is supposed that the pair of two-level atoms is laser cooled and trapped into the ground vibrational state, in which vibrational quantum number ⟨nv⟩=0\langle n_v\rangle =0⟨nv​⟩=0 . Two Jaynes–Cummings models are investigated. One is the Jaynes–Cummings model with intensity-dependent coupling and the another is the two-photon Jaynes–Cummings model of a pair of indistinguishable two-level atoms. It should be noted that in the present model, at initial moment t=0t=0t=0 , in intensity-dependent Jaynes–Cummings model the cavity field is prepared in Holstein–Primakoff SU(1,1) CS, while in two-photon Jaynes–Cummings model it is prepared in the squeezed vacuum state. Moreover, at initial moment t=0t=0t=0 , pair of atoms is supposed to be in the first excited state ∣e1⟩\vert e_1\rangle ∣e1​⟩ in both models. By using exact analytical solutions for state-vectors of the coupled atom-field systems amplitude-squared squeezing of the quantized cavity field is examined as a function of the ∣ξ∣\vert \xi \vert ∣ξ∣ parameter. In this situation, in both models higher-order squeezing has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.
Dynamics of nonclassicality in a generalized Tavis Cummings model with XY spin (1/2,1)(1/2,1)(1/2,1) atomic interactions
We investigate the dynamics of nonclassicality, quantified by the Wigner Yanase skew information, in generalized Jaynes Cummings (JC) and Tavis Cummings (TC) models describing light matter interactions in cavity quantum electrodynamics. We first analyze a generalized JC model consisting of a single bosonic cavity mode coupled to a spin 1 atom, focusing on the temporal evolution of nonclassicality in both the cavity field and the atomic subsystem. We then extend this framework to a generalized TC model by introducing an additional spin 1/21/21/2 atom, enabling us to examine the influence of collective atomic degrees of freedom. The global dynamics are investigated both with and without an XYXYXY spin interaction. Our results show that, under resonance conditions, the system exhibits efficient excitation exchange between the cavity field and the atomic subsystem, resulting in regular, coherent nonclassicality dynamics and enhanced field nonclassicality generation. Conversely, an increasing longitudinal magnetic field acts primarily as an effective detuning parameter rather than a direct exchange interaction. In this off resonant regime, the atom field coupling is substantially weakened, localizing excitations within the atomic subsystem. This localization suppresses coherent energy transfer to the cavity field, leading to a pronounced reduction in field nonclassicality, while the atomic subsystem retains the majority of the quantum correlations. Notably, atomic superposition states exhibit highly irregular spin dynamics, reflecting a detuning-induced redistribution of quantum correlations. These findings demonstrate that the dynamics of spin and field nonclassicality are governed primarily by interaction mediated excitation flow and resonance conditions rather than the initial energy distribution alone, ..
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.