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arXiv:0809.1914 · New Journal of Physics

Nanomechanical-resonator-assisted induced transparency in a Cooper-pair box system

Xiao-Zhong Yuan, Hsi‐Sheng Goan, Chien-Hung Lin, Ka-Di Zhu, Yi-Wen Jiang

Published Sep 30, 2008• 17 citations
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Abstract

We propose a scheme to demonstrate the electromagnetically induced transparency (EIT) in a system consisting of a superconducting Cooper-pair box (CPB) coupled to a nanomechanical resonator (NR). In this scheme, the NR plays an important role to contribute additional auxiliary energy levels to the CPB so that the EIT phenomenon could be realized in such a system. We call it, in this paper, resonator-assisted induced transparency (RAIT). The RAIT technique provides a detection scheme in a real experiment to measure physical properties, such as the vibration frequency and the decay rate, of the coupled NR.

DOI
10.1088/1367-2630/10/9/095016

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We propose a scheme to demonstrate the electromagnetically induced transparency (EIT) in a system consisting of a superconducting Cooper-pair box (CPB) coupled to a nanomechanical resonator (NR). In this scheme, the NR plays an important role to contribute additional auxiliary energy levels to the CPB so that the EIT phenomenon could be realized in such a system. We call it, in this paper, resonator-assisted induced transparency (RAIT). The RAIT technique provides a detection scheme in a real experiment to measure physical properties, such as the vibration frequency and the decay rate, of the coupled NR.
We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.
We show two effects as a result of considering the second-order correction to the spectrum of a nanomechanical resonator electrostatically coupled to a Cooper-pair box. The spectrum of the Cooper-pair box is modified in a way which depends on the Fock state of the resonator. Similarly, the frequency of the resonator becomes dependent upon the state of the Cooper-pair box. We consider whether these frequency shifts could be utilized to prepare the nanomechanical resonator in a Fock state, to perform a quantum non-demolition measurement of the resonator Fock state, and to distinguish the phase states of the Cooper-pair box.
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.
We propose a scheme for generating squeezed states in solid state circuits consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair box (CPB) and a superconducting transmission line resonator (STLR). The nonlinear interaction between the NMR and the STLR can be implemented by setting the external biased flux of the CPB at certain values. The interaction Hamiltonian between the NMR and the STLR is derived by performing Fro¨\rm\ddot oo¨hlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian. The CPB plays the role of ``nonlinear media", and the squeezed states of the NMR can be easily generated in a manner similar to the three-wave mixing in quantum optics. This is the three-wave mixing in a solid-state circuit.
We study a hybrid nanomechanical system coupled to a spin ensemble as a quantum simulator to favor a quantum interference effect, electromagnetically induced transparency (EIT). This system consists of two nanomechanical resonators (NAMRs), each of which is coupled to a nuclear spin ensemble, and can be regarded as a crucial element in the quantum network of NAMR arrays coupled to spin ensembles. Here, the nuclear spin ensembles behave as a long-lived transducer to store and transfer the NAMRs' quantum information. This system shows the analog of the EIT effect under the driving of a probe microwave field. The double EIT phenomenon emerges in the large-NNN (the number of nuclei) limit within the low excitation approximation, because the interactions between the spin ensemble and the two NAMRs are reduced to the coupling of three harmonic oscillators. Furthermore, the group velocity is reduced in the two absorption windows.