Coherence Times of Dressed States of a Superconducting Qubit under Extreme Driving
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Abstract:
We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their dressed gap as a function of photon number and microwave amplitude, finding good agreement with theory. In addition, we extract the relaxation and dephasing rates of these states.Keywords:
Charge qubit
Dephasing
Flux qubit
Cooper pair
A superconducting qubit implementation is proposed that takes the advantage of both charge and phase degrees of freedom. Superpositions of flux states in a superconducting loop with three Josephson junctions form the states of the qubit. The charge degree of freedom is used to readout and couple the qubits. Cancellation of the first order coupling to the environment, at the working point of the qubit, protects it from the decoherence due to charge and flux fluctuations.
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Charge qubit
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We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
Charge qubit
Cooper pair
Flux qubit
Superconducting tunnel junction
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We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model for characterizing the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.
Flux qubit
Charge qubit
Relaxation oscillator
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Flux qubit
Charge qubit
Magnetic flux quantum
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We study the novel nonlinear phenomena that emerge in a charge qubit due to the interplay between a strong microwave flux drive and a periodic Josephson potential. We first analyse the system in terms of the linear Landau–Zener–Stückelberg model, and show its inadequacy in a periodic system with several Landau–Zener crossings within a drive period. Experimentally, we probe the quasienergy levels of the driven qubit with an LC cavity, which requires the use of linear response theory. We show also that our numerical calculations are in good agreement with the experimental data.
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Charge qubit
Zener diode
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We measure the coherence of a new superconducting qubit, the {\em low-impedance flux qubit}, finding $T_2^* \sim T_1 \sim 1.5\mu$s. It is a three-junction flux qubit, but the ratio of junction critical currents is chosen to make the qubit's potential have a single well form. The low impedance of its large shunting capacitance protects it from decoherence. This qubit has a moderate anharmonicity, whose sign is reversed compared with all other popular qubit designs. The qubit is capacitively coupled to a high-Q resonator in a $\lambda/2$ configuration, which permits the qubit's state to be read out dispersively.
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Charge qubit
Coherence time
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We investigate the pure dephasing of a Josephson qubit due to the spectral diffusion of two-level systems that are close to resonance with the qubit. We identify the parameter regime in which this pure dephasing rate can be of the order of the energy relaxation rate and, thus, the relation $T_2 = 2 T_1$ is violated for the qubit. This regime is reached if the dynamics of the thermal TLSs responsible for the spectral diffusion is sufficiently slower than the energy relaxation of the qubit. By adding periodic bias modulating the qubit frequency or TLS excitation energies we show that this pure dephasing mechanism can be mitigated, allowing enhancement of superconducting qubits coherence time. Mitigating pure dephasing, even if it is subdominant, is of special significance in view of recent suggestions for converting the dominant relaxation process ($T_1$) into erasure errors, leaving pure dephasing as the bottleneck for efficient quantum computation.
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Flux qubit
Charge qubit
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A simple microscopic model of a small superconducting loop interrupted by Josephson junction (flux qubit) allows to compute from the experimental data of Wal et.al \cite{Wal} an important parameter - the density of Cooper pairs at zero temperature. This density is determined by the cut-off energy in the BCS model and agrees with the original BCS suggestion but is lower by two orders of magnitude than the value accepted in the modern literature. The immediate consequences of this result are: the validity of the strong coupling BCS model, a plausible picture of electrons recombination into Cooper pairs, and a much weaker condition for the appearance of high-temperature superconductivity. Another consequence is that the popular interpretation of Josephson qubits as macroscopic quantum systems is replaced by a picture of qubit states being superpositions of the ground state and the state containing only a single excited Cooper pair.
Flux qubit
Cooper pair
Charge qubit
BCS theory
Superconducting tunnel junction
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The fluxonium qubit has arisen as one of the most promising candidate devices for implementing quantum information in superconducting devices, since it is both insensitive to charge noise (like flux qubits) and insensitive to flux noise (like charge qubits). Here, we investigate the stability of the quantum information to quasiparticle tunneling through a Josephson junction. Microscopically, this dephasing is due to the dependence of the quasiparticle transmission probability on the qubit state. We argue that on a phenomenological level the dephasing mechanism can be understood as originating from heat currents, which are flowing in the device due to possible effective temperature gradients, and their sensitivity to the qubit state. The emerging dephasing time is found to be insensitive to the number of junctions with which the superinductance of the fluxonium qubit is realised. Furthermore, we find that the dephasing time increases quadratically with the shunt-inductance of the circuit which highlights the stability of the device to this dephasing mechanism.
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Flux qubit
Charge qubit
Superconducting tunnel junction
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We study the influence of screening effect on quantum decoherence for charge qubit and the process of quantum information storage. When the flux produced by the circulating current in SQUID loop is considered, screening effect is formally characterized by a LC resonator. Using large-detuning condition and Fröhlich transformation in the qubit-cavity-resonator system, we calculate the decoherence factor for charge qubit and the effective qubit-cavity Hamiltonian. The decoherence factor owns a factorized structure, it shows that screening effect is a resource of decoherence for charge qubit. The effective Hamiltonian shows that the screening effect results in a frequency shift for charge qubit and a modified qubit-cavity coupling constant induced by a LC resonator.
Charge qubit
Flux qubit
Hamiltonian (control theory)
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