Models of Environment andT1Relaxation in Josephson Charge Qubits

Abstract

A theoretical interpretation of the recent experiments of Astafiev et. al. on the T1-relaxation rate in Josephson Charge Qubits is proposed. The experimentally observed reproducible nonmonotonic dependence of T1 on the splitting EJ of the qubit levels suggests further specification of the previously proposed models of the background charge noise. From our point of view the most promising is the "Andreev fluctuator" model of the noise. In this model the fluctuator is a Cooper pair that tunnels from a superconductor and occupies a pair of localized electronic states. Within this model one can naturally explain both the average linear T1(EJ ) dependence and the irregular fluctuations. PACS numbers:Proposals to implement qubits using superconducting nanocircuits have undergone an amazing development during the last years [1,2,3,4,5]. In Josephson Charge Qubit (JCQ) information is encoded in the charge states of a Cooper pair box. The JCQ is manipulated by tuning gate voltage and magnetic flux. Both time resolved coherent oscillations in single and coupled JCQ have been recently observed [2,6]. Although decoherence is a severe limitation to the performances of these devices the dominant source of noise is yet to be identified. A significant step towards a characterization of the environment in a JCQ has been recently made by Astafiev et.al.[7] The experimental set-up consists of a Cooper pair box connected to a reservoir through a tunnel junction of SQUID geometry with Josephson energy E J pierced by an external magnetic field. Provided that E c ≫ E J ≫ T (where E c , E J and T are correspondingly charging energy, Josephson energy and temperature, k B = = 1). only two charge states |0 and |1 are relevant and the Hamiltonian of the box reads:where, C g is the gate capacitance, V g is the gate voltage and e denotes the electron charge. In the rotated basis {|+ , |− } the Hamiltonian (1) reads:where E = δE 2 c + E 2 J and θ = arctan(E J /δE c ). One can distinguish the off degeneracy working points (θ ≈ 0 and δE c ≫ E J ) and the degeneracy one (θ = π/2 and δE c = 0). Astafiev et.al.[7] measured the energy relaxation rate Γ 1 of the JCQ in a wide range of parameters. Two main features have been observed: (*) Linear increase of Γ 1 with E J at large E J , and (**) Small nonmonotonous fluctuations in the Γ 1 (E J )-function on this linear background.We do not believe that the existing experimental information is sufficient to identify a unique interpretation. However, it substantially reduces the range of possibilities. In this Letter we show that some models which have been used to study dephasing in JCQ can not explain these features. We propose a model where all of them appear naturally.Many different mechanisms can be responsible for decoherence in JCQ. We will consider three models, all based on the idea that the oxide layer close to some metallic reservoir, like one of the leads or gates or Cooper pair box itself, is disordered and thus hosts trapping centers, i.e. localized states for the electrons.

Low- and High-Frequency Noise from Coherent Two-Level Systems

“…It is useful to relate our phenomenological results to the recent work of Faoro et al [7], where they considered physical models of the fluctuators, which could couple to and relax qubits. They considered three models: (I) a single electron trap in tunnel contact with a metallic gate, (II) a single electron occupying a double trap, and (III) a double trap that can absorb/emit a Cooper pair from the qubit or a superconducting gate.…”

“…The distribution is log-uniform in the tunnel splitting and linear in the bias. Microscopically, this distribution may describe double traps or "Andreev fluctuators" considered recently by Faoro et al [7] in their study of the relaxation (T 1 decay) of Josephson qubits due to the high-frequency noise. Our results are obtained for environments with a large number of TLSs which are weakly coupled to the qubit.…”

Superconducting Qubits II: Decoherence

“…A number of studies of models taking this aspect into account have been published (Paladino et al, 2002;Grishin et al, 2005;Shnirman et al, 2005;Galperin et al, 2003;Faoro et al, 2005;de Sousa et al, 2005). A highly simplified version is to still take the Gaussian assumption but realize that there is always a slowest fluctuator, thus the integrals in K f (t) can be cut off at some frequency ω IR at the infrared (low frequency) end of the spectrum, i.e.…”

Josephson Qubits as Probes of 1/f Noise

“…It is useful to relate our phenomenological results to the recent work of Faoro et al [28], de Sousa et al [29], Grishin et al [30], and Faoro et al [31], where physical models of the fluctuators, coupling to and relaxing the qubit, were considered. In Ref.…”

“…In Ref. [28] three models were studied: (I) a single electron trap in tunnel contact with a metallic gate, (II) a single electron occupying a double trap, and (III) a double trap that can absorb/emit a Cooper pair from the qubit or a superconducting gate ('Andreev fluctuator'). In all models a uniform distribution of the trap energy levels was assumed.…”