Quantum nondemolition measurements of a flux qubit coupled to a noisy detector

We theoretically study the quantum nondemolition measurements of a flux qubit coupled to a noisy superconduct-ing quantum interference device (SQUID).The obtained analytical results indicate that the measurement probability is frequency-dependent in a short time scale and has a close relationship with the measurement-induced dephasing.Furthermore,when the detuning between the driven and bare resonator equals the coupling strength,we can obtain the maximum measurement rate that is determined by the character of the noise in the SQUID.Finally,we analysed the mixed effect caused by coupling between the non-diagonal term and the external variable.It is found that the initial information of the qubit is destroyed due to quantum tunneling between the qubit states.     

ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field

We have performed spectroscopy of a superconducting charge qubit coupled nonresonantly to a single mode of an on-chip resonator. The strong coupling induces a large ac Stark shift in the energy levels of both the qubit and the resonator. The dispersive shift of the resonator frequency is used to nondestructively determine the qubit state. Photon shot noise in the measurement field induces qubit level fluctuations leading to dephasing which is characteristic for the measurement backaction. A crossover in line shape with measurement power is observed and theoretically explained. For weak measurement a long intrinsic dephasing time of T2>200 ns of the qubit is found.     

Circuit QED with a nonlinear resonator: ac-Stark shift and dephasing

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.     

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED

We investigate theoretically the dynamical behavior of a qubit obtained with the two ground eigenstates of an ultrastrong coupling circuit-QED system consisting of a finite number of Josephson fluxonium atoms inductively coupled to a transmission line resonator. We show a universal set of quantum gates by using multiple transmission line resonators (each resonator represents a single qubit). We discuss the intrinsic "anisotropic" nature of noise sources for fluxonium artificial atoms. Through a master equation treatment with colored noise and many-level dynamics, we prove that, for a general class of anisotropic noise sources, the coherence time of the qubit and the fidelity of the quantum operations can be dramatically improved in an optimal regime of ultrastrong coupling, where the ground state is an entangled photonic "cat" state.     

Sisyphus effects in a microwave-excited flux-qubit resonator system

Sisyphus amplification, familiar from quantum optics, has recently been reported as a mechanism to explain the enhanced quality factor of a classical resonant (tank) circuit coupled to a superconducting flux qubit. Here we present data from a coupled system, comprising a quantum mechanical rf SQUID (flux qubit) reactively monitored by an ultrahigh quality factor noise driven rf resonator and excited by microwaves. The system exhibits enhancement of the tank-circuit resonance, bringing it significantly closer (within 1%) to the lasing limit, than previously reported results.     

Synchronization and bistability of a qubit coupled to a driven dissipative oscillator

We study numerically the behavior of a qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of the number of photons in the resonator. The lifetimes in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with the appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev, Nature (London) 449, 588 (2007)].     

Approaching unit visibility for control of a superconducting qubit with dispersive readout

In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 95% can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. In a measurement of Ramsey fringes, the qubit coherence time is larger than 500 ns.     

Generating Squeezed States of Nanomechanical Resonator via a Flux Qubit in a Hybrid System

We propose a scheme for generating squeezed states based on a superconducting hybrid system.Our system consists of a nanomechanical resonator,a superconducting flux qubit,and a superconducting transmission line resonator.Using our proposal,one can easily generate the squeezed states of the nanomechanical resonator.In our scheme,the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as 'nonlinear media' with a tunable Josephson energy.The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state,which can greatly decrease the effect of the decoherence of the flux qubit on the squeezed efficiency.     

Integrated superconducting circuit for qubit and resonator protection

A semi-infinite waveguide acts as a mirror and helps protect the qubit in front of it from decoherence. Here, we investigate the interference effect in an open waveguide consisting of resonators with different decay rates. We find that a lossy resonator works as a mirror and changes the effective decay rate of the other. The spontaneous radiation of qubit is related to its environment, and we can control it by arranging the lossy resonator's position or frequency. Our approach helps improving the qubit performance, as well as the quantum gate fidelities.     

Tunneling spectroscopy of two-level systems inside a Josephson junction

We consider a two-level system (TLS) with energy level separation plankvOmega0 inside a Josephson junction. The junction is shunted by a resistor R and is voltage V biased. If the TLS modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance 2eV=plankvOmega0. The Rabi oscillations, in turn, translate into oscillations of current and voltage that can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit.     

Quantum dynamics of a mechanical resonator driven by a cavity

We explore the quantum dynamics of a mechanical resonator whose position is coupled to the frequency of an optical (or microwave) cavity mode. When the cavity is driven at a frequency above resonance the mechanical resonator can gain energy and for sufficiently strong coupling this results in limit-cycle oscillations. Using a truncated Wigner function approach, which captures the zero-point fluctuations in the system, we develop an approximate analytic treatment of the resonator dynamics in the limit-cycle regime. We find that the limit-cycle oscillations produced by the cavity are associated with rather low levels of energy fluctuations in the resonator. Compared to a resonator at the same temperature which is driven by a pure harmonic drive to a given average energy, the cavity-driven oscillations can have much lower energy fluctuations. Furthermore, at sufficiently low temperatures, the cavity can drive the resonator into a non-classical state which is number-squeezed.     

Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms

We present results on a circuit QED experiment in which a separate transmission line is used to address a quasilumped element superconducting microwave resonator which is in turn coupled to an Al/AlO(x)/Al Cooper-pair box charge qubit. With our device, we find a strong correlation between the lifetime of the qubit and the inverse of the coupling between the qubit and the transmission line. At the smallest coupling we measured, the lifetime of the Cooper-pair box was T?=200 μs, which represents more than a twentyfold improvement in the lifetime of the Cooper-pair box compared with previous results. These results imply that the loss tangent in the AlO(x) junction barrier must be less than about 4×10?? at 4.5 GHz, about 4 orders of magnitude less than reported in larger area Al/AlO(x)/Al tunnel junctions.     

Hybrid quantum circuit with a superconducting qubit coupled to a spin ensemble

We report the experimental realization of a hybrid quantum circuit combining a superconducting qubit and an ensemble of electronic spins. The qubit, of the transmon type, is coherently coupled to the spin ensemble consisting of nitrogen-vacancy centers in a diamond crystal via a frequency-tunable superconducting resonator acting as a quantum bus. Using this circuit, we prepare a superposition of the qubit states that we store into collective excitations of the spin ensemble and retrieve back into the qubit later on. These results constitute a proof of concept of spin-ensemble based quantum memory for superconducting qubits.     

Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics

Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution.     

Synchronizing Two Superconducting Qubits through a Dissipating Resonator

A system consisting of two qubits and a resonator is considered in the presence of different sources of noise, bringing to light the possibility of making the two qubits evolve in a synchronized way. A direct qubit–qubit interaction turns out to be a crucial ingredient, as well as the dissipation processes involving the resonator. The detrimental role of the local dephasing of the qubits is also taken into account.     

Controllable strong coupling between individual spin qubits and a transmission line resonator via nanomechanical resonators

We investigate a hybrid quantum system where an individual electronic spin qubit (EQ) and a transmission line resonator (TLR) are connected by a nanomechanical resonator (NAMR). We analyze the possibility of realizing a strong coupling between the EQ and the TLR. Compared with a direct coupling between an EQ and a TLR, the achieved coupling can be stronger and controllable. The proposal might be used to implement a high-fidelity quantum state transfer between the spin qubit and the TLR, and is scalable to involve several individual EQ-NAMR coupled systems with a TLR.     

Entropy Correlations and Entanglement of a Superconducting Charge Qubitin a Resonant Cavity in the Presence of Noise

We study the dynamics of the entropy correlations and entanglement in a system of interaction of a superconducting charge qubit with a single-mode resonant cavity subject to noise considered as two-state random phase telegraph noise. We show that although the noise has an apparent suppressing effect on the evolution of the entropies of the qubit and the field and also on the entanglement in the system, the entropy exchange between the qubit and the
field is independent of it during the time evolution of the system.     

Theory of microwave parametric down-conversion and squeezing using circuit QED

We study theoretically the parametric down-conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper-pair box (CPB) qubit located inside a transmission line resonator. The nonlinear susceptibility chi2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% approximately 13 dB below the vacuum noise level should be readily achievable.     

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.