Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown to acquire an additional phase called Berry's phase, in addition to the usual dynamical phase. This phase has been found in two-level quantum systems intrinsic to many superconducting qubits and has particularly been calculated for the charge, flux and Josephson phase qubit. Here, we present an alternative derivation of the Berry's phase in a current-biased Josephson junction qubit. We also calculate the complete Berry's phase evaluated over a closed loop in a frequency parameter space and compare this with the geometric phase. From this comparison, we examine the possibility of using a single phase qubit for topological quantum computing.Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown to acquire an additional phase called Berry's phase, in addition to the usual dynamical phase. This phase has been found in two-level quantum systems intrinsic to many superconducting qubits and has particularly been calculated for the charge, flux and Josephson phase qubit. Here, we present an alternative derivation of the Berry's phase in a current-biased Josephson junction qubit. We also calculate the complete Berry's phase evaluated over a closed loop in a frequency parameter space and compare this with the geometric phase. From this comparison, we examine the possibility of using a single phase qubit for topological quantum computing.

arXiv:0909.2286Sep 12, 20090 citations

Eigenstates and eigenvalues of a current biased Josephson junction

Daniel N. Rogovin, Marlan O. Scully

Physics Letters ASep 1, 19800 citations

Measuring weak microwave signals via current-biased Josephson junctions: Approaching the quantum limit of energy detection

Y. Q. Chai, S. N. Wang, P. H. Ouyang +1 more

Single-photon detection is an energy quantum limit detection (EQLD) of extremely weak electromagnetic waves. Given that the sensitivity of the conventional electromagnetic induction microwave receiver working at room temperature is very limited, as a result of the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum ${d}_{\mathrm{KC}}$ index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.Single-photon detection is an energy quantum limit detection (EQLD) of extremely weak electromagnetic waves. Given that the sensitivity of the conventional electromagnetic induction microwave receiver working at room temperature is very limited, as a result of the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum ${d}_{\mathrm{KC}}$ index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.

arXiv:2410.23947Physical review. B./Physical review. BJan 2, 20256 citations

Eigenstates and eigenvalues of a current biased Josephson junction

Daniel N. Rogovin, Marlan O. Scully

Physics Letters AMar 1, 19801 citation

Ring Oscillators for Clocking Reversible Superconducting Circuits and Fabrication Process Benchmarking

Vasili K. Semenov, Yuri A. Polyakov, Sergey K. Tolpygo

Existing concepts of reversible superconducting circuits as well as demonstrated adiabatic circuits require three-phase bias/clock signals generated by room temperature sources. A while ago, we suggested that a multi-phase bias/clock could be provided by a local Josephson junction-based generator. The generator looks like a long annular Josephson junction, only composed of discreet elements - junctions and inductors, and closed into a ring via a flux pump to inject any required number of vortices into the ring. A steady motion of the vortices forced by a uniformly distributed dc bias current applied to the ring is accompanied by a nearly harmonic ac currents flowing via the Josephson junctions (JJs) connected in series with small inductors. These ac currents serve as multi-phase bias/clock for nSQUID-based circuitry. To verify this concept and compare the dissipated energy with kBTln2 threshold, we developed a ring composed of 256 unshunted JJs with 20 μA target critical current, Ic. We investigated the behavior of the ring oscillator at each vortex count from 0 to 256. The measured critical current of the ring with vortices was about 0.1 μA per one JJ, which can be explained by unavoidable nonuniformity of the ring components and the influence of fluxes frozen near the ring. The corresponding energy dissipation, about 10kBT per passage of one vortex through one JJ, should be reduced further for prospective experiments with reversible circuits. However, obtained I-V characteristics could be of interest for scientists working with long Josephson junctions. Superiority of the fabrication process used in this work is demonstrated by the obtained about 200 times reduction of Icof the ring with vortices with respect to a single comprising JJ, much larger than in any previously described case.Existing concepts of reversible superconducting circuits as well as demonstrated adiabatic circuits require three-phase bias/clock signals generated by room temperature sources. A while ago, we suggested that a multi-phase bias/clock could be provided by a local Josephson junction-based generator. The generator looks like a long annular Josephson junction, only composed of discreet elements - junctions and inductors, and closed into a ring via a flux pump to inject any required number of vortices into the ring. A steady motion of the vortices forced by a uniformly distributed dc bias current applied to the ring is accompanied by a nearly harmonic ac currents flowing via the Josephson junctions (JJs) connected in series with small inductors. These ac currents serve as multi-phase bias/clock for nSQUID-based circuitry. To verify this concept and compare the dissipated energy with kBTln2 threshold, we developed a ring composed of 256 unshunted JJs with 20 μA target critical current, Ic. We investigated the behavior of the ring oscillator at each vortex count from 0 to 256. The measured critical current of the ring with vortices was about 0.1 μA per one JJ, which can be explained by unavoidable nonuniformity of the ring components and the influence of fluxes frozen near the ring. The corresponding energy dissipation, about 10kBT per passage of one vortex through one JJ, should be reduced further for prospective experiments with reversible circuits. However, obtained I-V characteristics could be of interest for scientists working with long Josephson junctions. Superiority of the fabrication process used in this work is demonstrated by the obtained about 200 times reduction of Icof the ring with vortices with respect to a single comprising JJ, much larger than in any previously described case.

arXiv:1704.08176IEEE International Superconductive Electronics Conference (ISEC)Jun 1, 20172 citations

Macroscopic Quantum Effects in the Current-Biased Josephson Junction

Michel Devoret, Daniel ESTEVE, C. Urbina +3 more

Modern problems in condensed matter sciencesJan 1, 19929 citations

{d}_{\mathrm{KC}}

index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.