Perturbative approach to the capacitive interaction between a sensor quantum dot and a charge qubit

Abstract

We consider the capacitive interaction between a charge qubit and a sensor quantum dot(SQD) perturbatively to the second order of their coupling constant at zero temperature by utilizing the method of non-equilibrium Green's functions together with infinite-U Lacroix approximation and employing Majorana fermion representation for qubit isospin operators. The effect of back-actions on dynamics of the system is taken into account by calculating the self-energies and the Green's functions in a self-consistent manner. To demonstrate the applicability of the method, we investigate relevant physical quantities of the system at zero and finite bias voltages. In the regime of weak SQD-qubit coupling, we find a linear relation between the stationary-state expectation values of the third component of the qubit isospin vector, $⟨{\tau }_3⟩$, and the differential conductance of the SQD. Furthermore, our numerical results predict that the effect of SQD-qubit coupling on differential conductance of the SQD should be maximized at zero bias voltage. Moreover, we obtain an analytical expression to describe the behavior of the differential conductance of the SQD with respect to the qubit parameters. Our results at zero bias voltage are consistent with the results of numerical renormalization group method.

9 pages, 6 figures, submitted to PRB

References in corpus (11)

• Single-shot read-out of an individual electron spin in a quantum dot
• The numerical renormalization group method for quantum impurity systems
• Relaxation and Zeno effect in qubit measurements
• Measurement efficiency and n-shot read out of spin qubits
• Spin-spin correlators in Majorana representation
• Anderson Model out of equilibrium: decoherence effects in transport through a quantum dot
• Qubit measurements with a double-dot detector
• Quantum mechanical approach to decoherence and relaxation generated by fluctuating environment
• Detection of the relaxation rates of an interacting quantum dot by a capacitively coupled sensor dot
• Quantum dynamics in nonequilibrium environments
• Qubit quantum-dot sensors: noise cancellation by coherent backaction, initial slips, and elliptical precession