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Photonics Letters of Poland

The study of entropy in a transmission line resonator interacting with a capacitively coupled Cooper pair box

Clodoaldo Valverde, B. Baseia

Published Sep 30, 2019• 0 citations
Publisher

Abstract

In the present work, we theoretically study the entropy of a Cooper pair box coupled to a one-dimensional transmission line resonator. The proposed scheme uses the Jaynes-Cummings model in presence of losses to study the time avolution of the system entropy. The coupling of these two subsystems provides an important indication of the influence of Cooper pair box on the evolution of system entropy. Decaying CPB allows us to control variation of entropy at certain times.

DOI
10.4302/plp.v11i3.921

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In the present work, we theoretically study the entropy of a Cooper pair box coupled to a one-dimensional transmission line resonator. The proposed scheme uses the Jaynes-Cummings model in presence of losses to study the time avolution of the system entropy. The coupling of these two subsystems provides an important indication of the influence of Cooper pair box on the evolution of system entropy. Decaying CPB allows us to control variation of entropy at certain times.
Abstract The present work investigates the entropy and the excitation inversion of a coupled system that consists of a qubit represented by a Cooper pair box (CPB) interacting with a transmission line working as a circuit quantum electrodynamics (CQED). The proposed scheme uses the Buck-Sukumar model with a time dependent frequency in the presence of losses to study the evolution of the entropy and the excitation inversion of the system. We have shown that the CQED is much more sensitive to the presence of losses than the CPB. The results also show that it is possible to monitor properties of the subsystems through appropriate choices of the time-dependent parameters.
We calculate the dynamics of a nanomechanical oscillator (NMO) coupled capacitively to a Cooper-pair box (CPB) by solving a stochastic Schr\"odinger equation with two Lindblad operators [Commun. Math. Phys. 48, 119 (1976).]. Both the NMO and the CPB are assumed dissipative, and the coupling is treated within the rotating wave approximation. We show numerically that, if the CPB decay time is smaller than the NMO decay time, the coupled NMO will lose energy faster and the coupled CPB more slowly than the uncoupled NMO and CPB do. The results show that the efficiency of energy loss by an NMO can be substantially increased if the NMO is coupled to a CPB.
We propose a scheme to implement quantum information transfer between Cooper-pair boxes (CPBs) in a circuit quantum electrodynamic (QED) system with Landau—Zener tunneling. The system consists of two CPB qubits and a one-dimensional transmission line resonator (TLR). By analytically solving the eigenequation and numerically calculating the transition probability, the results show the quantum state transfer from one qubit to another via a fast adiabatic passage. The coupling mechanism is robust against decoherence effects.
We propose an experimental procedure to directly measure the state of an electromagnetic field inside a resonator, corresponding to a superconducting transmission line, coupled to a Cooper-pair box (CPB). The measurement protocol is based on the use of a dispersive interaction between the field and the CPB, and the coupling to an external classical field that is tuned to resonance with either the field or the CPB. We present a numerical simulation that demonstrates the feasibility of this protocol, which is within reach of present technology.
We investigate the action of time-dependent detunings upon the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator. The method employs the Jaynes-Cummings model with damping, assuming different decay rates of the Cooper pair box and various fixed and time-dependent detunings. It is shown that, when the presence of damping plus constant detunings destroys the collapse/revival effects, convenient choices of time-dependent detunings allow one to reconstruct such events in a perfect way. It is also shown that the mean excitation of the nanomechanical resonator is more robust against damping of the Cooper pair box for convenient values of time-dependent detunings.