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Modern Physics Letters B

Generating squeezed states of a nanomechanical resonator via a charge qubit in a hybrid system

Chao-Quan Wang, Jian Zou, Zhi‐Ming Zhang

Published Nov 15, 2017• 0 citations
Publisher

Abstract

We propose a scheme for generating squeezed states of a nanomechanical resonator. The scheme is based on a hybrid system consisting of two NAMRs and a superconducting charge qubit (SCCQ). The nonlinear interaction between the two nanomechanical resonators (NAMRs) can be implemented by setting the external biased flux of the SCCQ at some certain values, which plays the role of “nonlinear media”. The noise in the SCCQ does not need to be considered, since we can adiabatically keep the SCCQ at the ground state. In addition, the squeezing parameters can also be adjusted by changing the external driving voltage.

DOI
10.1142/s0217984917503432

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We propose a scheme for generating squeezed states of a nanomechanical resonator. The scheme is based on a hybrid system consisting of two NAMRs and a superconducting charge qubit (SCCQ). The nonlinear interaction between the two nanomechanical resonators (NAMRs) can be implemented by setting the external biased flux of the SCCQ at some certain values, which plays the role of “nonlinear media”. The noise in the SCCQ does not need to be considered, since we can adiabatically keep the SCCQ at the ground state. In addition, the squeezing parameters can also be adjusted by changing the external driving voltage.
We propose a scheme for generating squeezed states based on a superconducting hybrid system. Our system consists of a nanomechanical resonator, a superconducting flux qubit, and a superconducting transmission line resonator. Using our proposal, one can easily generate the squeezed states of the nanomechanical resonator. In our scheme, the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as 'nonlinear media' with a tunable Josephson energy. The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state, which can greatly decrease the effect of the decoherence of the flux qubit on the squeezed efficiency.
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 propose a scheme for generating squeezed states of nanomechanical resonator in a solid state circuit system which consists of a nanomechanical resonator, a superconducting Cooper-pair box, and a superconducting transmission line resonator. The nonlinear interaction between the nanomechanical resonator and superconducting transmission line resonator can be implemented by setting the external biased flux of the Cooper-pair box at some special values. The squeezed states of the nanomechanical resonator can be generated by degenerate three-wave mixing and the Cooper-pair box plays the role of “nonlinear medium” in the squeezing process.
A scheme for generating the Schrödinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit is proposed. The charge qubit, driven by two strong classical fields, interacts with a high‐frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit. This generates the entangled cat state between the NAMR and charge qubit, and the NAMR cat state can be achieved after some operations applied on this entangled cat state. The robustness of the scheme is justified by considering noise from environment, and the feasibility of the scheme is discussed.
We propose a scheme for generating squeezed states in solid state circuits which consist a superconducting transmission line resonator (STLR), a superconducting Cooper-pair box (CPB) and a nanoelectromechanical resonator (NMR). The nonlinear interaction between the STLR and the CPB can be implemented by setting the external biased flux of the CPB at some certain points. The interaction Hamiltonian between the STLR and the NMR is derived by performing Frohlich 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, and the squeezed states of the STLR can be easily generated, which is similar to the three-wave mixing in quantum optics.
Abstract We propose a scheme for realizing quadrature squeezing of the mechanical mode in a superconducting electromechanical system, where a nanomechanical resonator (NAMR) is coupled to a superconducting transmission line resonator (STLR) via a superconducting quantum interference device (SQUID), and the SQUID acts as a qubit. Under a large detuning condition, we use the Fröhlich-Nakajima transformation to adiabatically eliminate the qubit and obtain an effective Hamiltonian for the STLR and the NAMR. Our results show that a strong squeezing effect (beyond 3 dB limit) can occur in the NAMR, and the squeezing degree can be optimized by controlling the strength of the driving field and the dissipation ratio of the system. One of the most notable features of our results is the universality, i.e. the results only depend on a few scaled quantities, not on too many parameters.