Cooper-pair qubit and Cooper-pair electrometer in one device

Abstract

An all-superconductor charge qubit enabling a radio-frequency readout of its quantum state is described. The core element of the setup is a superconducting loop which includes the single-Cooperpair (Bloch) transistor. This circuit has two functions: First, it operates as a charge qubit with magnetic control of Josephson coupling and electrostatic control of the charge on the transistor island. Secondly, it acts as the transducer of the rf electrometer, which probes the qubit state by measuring the Josephson inductance of the transistor. The evaluation of the basic parameters of this device shows its superiority over the rf-SET-based qubit setup.PACS numbers: 74.50.+r, 85.25.Na, 03.67.Lx Superconducting structures with small Josephson tunnel junctions serve as a basis for electronic devices operating on single Cooper pairs and possessing remarkable characteristics. The paper Ref.[1] has demonstrated the potential of the single-Cooper-pair box circuit [2] as a charge qubit and thus has attracted renewed attention to this field. The practical realization of the Cooper pair qubit is not, however, simple and the main problems here are the achievement of a reliable readout of the quantum state and an elongation of the decoherence time. For the most part, these two issues are interrelated because a charge detector coupled to the qubit presents the principal source of quantum decoherence.The qubit setup consisting of a Cooper pair box and a capacitively coupled single electron transistor (SET, including the rf-SET [3]) has been extensively explored [4,5,6]. Although a preliminary analysis shows that qubit states can, in principle, be measured in the snapshot regime [6], the 'mismatch' of the charge carriers in the setup components (namely, the incoherent nature of charges in the SET) might lead to an unaccounted enhancement of decoherence in the system. Alternatively, the generic type of Cooper-pair (Bloch-transistor [7]) electrometers made from superconductors [8,9] seems to be quite promising as regards matching with the Cooper pair box. Furthermore, similar to dc-SQUIDs [10] and in contrast to SETs, the resistively shunted Cooper-pair electrometer belongs to the category of perfect (quantumlimited) linear detectors [11,12] and, therefore, can perform continuous measurements of a quantum object [13].Recently, we have proposed an rf-driven single-Cooperpair electrometer [14] whose energy-resolution figure ǫ can approach the standard quantum limit of /2. The transducer of this electrometer is a Bloch transistor inserted into a superconducting loop. The magnitude of the supercurrent circulating in the loop depends on the polarization charge (quasicharge) on the transistor island induced via a coupling capacitance by the charge source, e.g., the qubit.In this paper we present a circuit in which the electrometer's transducer takes over the function of the Cooper pair box (qubit) as well. The device's core el- ement is a superconducting loop including a mesoscopic double Josephson junction with a capacitive gate (transis...

Current-phase relation and Josephson inductance in a superconducting Cooper-pair transistor

“…͑2͒ have to be solved first. 15,16 Qualitative analysis can be performed in the charge basis taking only two charge states into account. Then, the Hamiltonian can be written in terms of Pauli spin matrices as…”

The two-Josephson-junction flux qubit with large tunneling amplitude

“…Since successful demonstration of Rabi oscillations and Landau-Zener coherent effects [1][2][3][4][5] , the superconducting qubits (quantum bits) based on mesoscopic Josephson junctions became the subject of consideration as possible candidates to be the basic elements of a quantum computer hardware 6,7 , including detectors to measure the state of an individual qubit [8][9][10][11][12] . The Josephson junction (JJ) qubits have two energy scales which are the Josephson coupling energy E J and the charging energy E C of the JJ, and they are subdivided into flux qubits, charge qubits, as well as charge-phase qubits.…”

Coupling and Dephasing in Josephson Charge-Phase Qubit with Radio Frequency Readout

“…As a result, the resonance frequencies take the distinct values for the ground and excited states, ω 0,1 = (L (0,1) eff C T ) −1/2 , and this property is used for the radio frequency readout of the qubit [1].…”

“…However, operation of these devices is usually associated with a significant exchange of energy between detector and qubit, so in order to avoid fast decoherence the detector must be reliably decoupled from the qubit at the time of quantum manipulation. Recently, the class of Josephson qubit detectors based on the measurement of the reactive component of electrical signals related to nonlinear behavior of the Josephson inductance has been extensively studied [1,2,3,4]. Due to specific coupling to the qubit variables The core of the qubit is the superconducting ring of small inductance L including two small tunnel junctions of capacitances C1 and C2 and Josephson coupling energies EJ1 and EJ2, respectively.…”

“…In this paper, we consider the charge-phase qubit [1] comprising a macroscopic superconducting ring including two small Josephson junctions with a small island in between (see Fig. 1), i.e., a Cooper pair box [6] of SQUID configuration.…”