Quantum Nondemolition Charge Measurement of a Josephson Qubit

In a qubit system, the measurement operator does not necessarily commute with the qubit Hamiltonian, so that the readout process demolishes (mixes) the qubit energy eigenstates. The readout time is therefore limited by such a mixing time and its fidelity will be reduced. A quantum nondemolition readout scheme is proposed in which the charge of a flux qubit is measured. The measurement operator is shown to commute with the qubit Hamiltonian in the reduced two-level Hilbert space, even though the Hamiltonian contains non-commuting charge and flux terms.Comment: 4 pages, 3 figures, a paragraph added to describe how the scheme works in charge regim

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc SQUID mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear, current dependent inductance, inducing an external flux tunable, nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive, radiation pressure type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state

Noncommutative fluid dynamics in the K\"{a}hler parametrization

In this paper, we propose a first order action functional for a large class of systems that generalize the relativistic perfect fluids in the K\"{a}hler parametrization to noncommutative spacetimes. We calculate the equations of motion for the fluid potentials and the energy-momentum tensor in the first order in the noncommutative parameter. The density current does not receive any noncommutative corrections and it is conserved under the action of the commutative generators $P_{\mu}$ but the energy-momentum tensor is not. Therefore, we determine the set of constraints under which the energy-momentum tensor is divergenceless. Another set of constraints on the fluid potentials is obtained from the requirement of the invariance of the action under the generalization of the volume preserving transformations of the noncommutative spacetime. We show that the proposed action describes noncommutative fluid models by casting the energy-momentum tensor in the familiar fluid form and identifying the corresponding energy and momentum densities. In the commutative limit, they are identical to the corresponding quantities of the relativistic perfect fluids. The energy-momentum tensor contains a dissipative term that is due to the noncommutative spacetime and vanishes in the commutative limit. Finally, we particularize the theory to the case when the complex fluid potentials are characterized by a function $K(z,\bar{z})$ that is a deformation of the complex plane and show that this model has important common features with the commutative fluid such as infinitely many conserved currents and a conserved axial current that in the commutative case is associated to the topologically conserved linking number.Comment: References fixed. Typos corrected. 12 page

Quantum Phase Tomography of a Strongly Driven Qubit

The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stueckelberg oscillations in qubit magnetization. The resulting oscillatory patterns are a hallmark of the coherent strongly-driven regime in qubits, quantum dots and other two-level systems. The two-dimensional Fourier transforms of these patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of qubit state and show that they can be used to probe dephasing mechanisms in the qubit.Comment: 5 pgs, 4 fg

Probing Decoherence with Electromagnetically Induced Transparency in Superconductive Quantum Circuits

Superconductive quantum circuits (SQCs) comprise quantized energy levels that may be coupled via microwave electromagnetic fields. Described in this way, one may draw a close analogy to atoms with internal (electronic) levels coupled by laser light fields. In this Letter, we present a superconductive analog to electromagnetically induced transparency (S-EIT) that utilizes SQC designs of present day experimental consideration. We discuss how S-EIT can be used to establish macroscopic coherence in such systems and, thereby, utilized as a sensitive probe of decoherence.Comment: 5 pages, 3 figure

Entanglement generation in persistent current qubits

In this paper we investigate the generation of entanglement between two persistent current qubits. The qubits are coupled inductively to each other and to a common bias field, which is used to control the qubit behaviour and is represented schematically by a linear oscillator mode. We consider the use of classical and quantum representations for the qubit control fields and how fluctuations in the control fields tend to suppress entanglement. In particular, we demonstrate how fluctuations in the bias fields affect the entanglement generated between persistent current qubits and may limit the ability to design practical systems.Comment: 7 pages, 4 figures, minor changes in reply to referees comment

Impact of time-ordered measurements of the two states in a niobium superconducting qubit structure

Measurements of thermal activation are made in a superconducting, niobium Persistent-Current (PC) qubit structure, which has two stable classical states of equal and opposite circulating current. The magnetization signal is read out by ramping the bias current of a DC SQUID. This ramping causes time-ordered measurements of the two states, where measurement of one state occurs before the other. This time-ordering results in an effective measurement time, which can be used to probe the thermal activation rate between the two states. Fitting the magnetization signal as a function of temperature and ramp time allows one to estimate a quality factor of 10^6 for our devices, a value favorable for the observation of long quantum coherence times at lower temperatures.Comment: 14 pages, 4 figure