Ya. S. Greenberg

Quantum behavior of a flux qubit coupled to a resonator

A detailed theory for a system of a superconducting qubit coupled to a transmission line resonator is presented. We describe the system by solving analytically and numerically the master equation for the density matrix, which includes a dissipative Lindblad term. We calculate the transmission coefficient, which provides a way to probe the dressed states of a qubit. The theoretical results are related to experiments with intermediate coupling between a qubit and a resonator when the coupling energy is of the same order as the qubit relaxation rate.

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.

Amplification and attenuation of a probe signal by doubly dressed states

We analyze a system composed of a qubit coupled to the electromagnetic fields in two high quality quantum oscillators. A particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonators harmonics. This doubly driven system can be described in terms of the doubly dressed qubit states. Our calculations demonstrate the possibility to change the number of photons in the resonator and the transmission of the fundamental-mode signal over a wide parameter range exploiting resonances with the dressed qubit. Experiments show that in the case of high quality resonators the dressed energy levels and corresponding resonance conditions can be probed, even for high driving amplitudes. The interaction of the qubit with photons of two harmonics can be used for the creation of quantum amplifiers or attenuators.

Low-frequency Rabi spectroscopy of dissipative two-level systems : Dressed-state approach

We have analyzed a dissipative two level quantum system (TLS) which is continuously and simultaneously irradiated by a high and low frequency excitation. The interaction of the TLS with a high frequency excitation is considered in the frame of the dressed state approach. A linear response of the coupled TLS and corresponding photon field system to a signal whose frequency is of the order of the Rabi frequency is found. The response exhibits undamped low frequency oscillations, whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the TLS. The method can be useful for low-frequency Rabi spectroscopy in various physical systems described by a two-level Hamiltonian, such as nuclei spins in NMR, double well quantum dots, superconducting flux and charge qubits, etc. The application of the method to a superconducting flux qubit and to the detection of NMR is considered in detail.

Integrated Thin-Film dc RSQUIDs for Noise Thermometry

Integrated thin-film dc RSQUIDs (Resistive Superconducting QUantum Interference Devices) have been developed that significantly simplify noise thermometer operation. We show theoretically that the main equations for noise thermometry deduced for rf RSQUIDs can also be applied to dc RSQUIDs. Our dc RSQUIDs can at least be operated down to 0.04 K. Between 0.14 and 5.9 K the measured noise temperature agrees with the temperature of calibrated reference thermometers. We investigate the errors and uncertainties of a dc RSQUID noise thermometer, in particular errors due to excess noise. A model for excess noise and its impact on the noise temperature is presented and shown to be in agreement with the measurements.

Theory of the voltage–current characteristics of high TC asymmetric DC SQUIDs

Abstract The theory developed previously for symmetric high T C DC SQUID is extended to account for different critical currents I C1 , I C2 and normal resistances R 1 , R 2 of Josephson junctions. The theory is based on analytical solution of a two-dimensional Fokker–Planck equation, which describes the dynamical behavior of DC SQUID in presence of thermal noise. The theory is valid for large inductance ( L >100 pH) high T C asymmetric DC SQUIDs with any values of critical currents of Josephson junctions and asymmetry parameters. The analytical expressions for the voltage modulation and for the shift of the voltage–flux curve under bias reversal are obtained. It is shown that the sensitivity of the voltage modulation to asymmetry of DC SQUID is strongly dependent on the level of thermal noise. The expression for the shift of voltage–flux curve can be used for the determination of the parameters of asymmetry from experimental dependencies.

Low-frequency Rabi spectroscopy for a dissipative two-level system

We have analyzed the interaction of a dissipative two-level quantum system with high- and low-frequency excitation. The system is continuously and simultaneously irradiated by these two waves. If the frequency of the first signal is close to the level separation, the response of the system exhibits undamped low-frequency oscillations whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the system. The method can be useful for low-frequency Rabi spectroscopy in various physical systems which are described by a two-level Hamiltonian, such as nuclei spins in NMR, double-well quantum dots, superconducting flux and charge qubits, etc. As examples, the application of the method to a nuclear spin and to the readout of a flux qubit are briefly discussed.

Theory of the voltage-current characteristic of high Tc DC SQUIDs

Abstract A new analytic theory for the voltage–current characteristic of symmetric high T c DC SQUIDs is developed. The theory is based on analytical solution of a two-dimensional Fokker–Planck equation, which describes the dynamical behavior of DC SQUID in presence of thermal noise. For high T c DC SQUIDs operating at 77 K with L >100 pH, where L is geometrical inductance of DC SQUID loop, our theory is valid for any values of critical currents of Josephson junctions and it allows a correct evaluation of transfer function of practical high T c DC SQUIDs. The theoretical voltage modulation is shown to be in a good agreement with the results of known computer simulations.

Flux qubit as a sensor of magnetic flux

We propose to use the quantum properties of a superconducting flux qubit in the construction of a magnetometer with quantum limited sensitivity. The main advantage of a flux qubit is that its noise is rather low, and its transfer functions relative to the measured flux can be made to be about 10mV/

Quantum signal transmission through a single-qubit chain

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