Observation of Resonant Tunneling between Macroscopically Distinct Quantum Levels

Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus cannot explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations," signaling quantum interference of macroscopically distinct states.

Strong correlations in quantum vortex nucleation of ultracold atomic gases

We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.

Parameter scaling in the decoherent quantum-classical transition for chaotic rf superconducting quantum interference devices

We numerically investigated the quantum-classical transition in rf-superconducting quantum interference device (SQUID) systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent lambda(m), exhibits nonmonotonic behavior as a function of the coupling strength D. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of lambda(m)/D. In addition, the scaling holds in SQUID systems to a relatively smaller variant Planck's over [symbol: see text], suggesting the universality for this scaling.

Probing noise in flux qubits via macroscopic resonant tunneling

Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than the target well. The rms amplitude of the noise, which is proportional to the dephasing rate 1/tauphi, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.

Macroscopic resonant tunneling in the presence of low frequency noise

We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with a significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.

Macroscopic tunnel splittings in superconducting phase qubits

Prototype Josephson-junction based qubit coherence times are too short for quantum computing. Recent experiments probing superconducting phase qubits have revealed previously unseen fine splittings in the transition energy spectra. These splittings have been attributed to new microscopic degrees of freedom (microresonators), a previously unknown source of decoherence. We show that macroscopic resonant tunneling in the extremely asymmetric double-well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data.

Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter

We investigate the experimental feasibility of realizing quantum information transfer (QIT) and entanglement with SQUID qubits in a microwave cavity via dark states. Realistic system parameters are presented. Our results show that QIT and entanglement with two-SQUID qubits can be achieved with a high fidelity. The present scheme is tolerant to device parameter nonuniformity. We also show that the strong coupling limit can be achieved with SQUID qubits in a microwave cavity. Thus, cavity-SQUID systems provide a new way for production of nonclassical microwave source and quantum communication.

Coherent temporal oscillations of macroscopic quantum states in a Josephson junction

We report the generation and observation of coherent temporal oscillations between the macroscopic quantum states of a Josephson tunnel junction by applying microwaves with frequencies close to the level separation. Coherent temporal oscillations of excited state populations were observed by monitoring the junction's tunneling probability as a function of time. From the data, the lower limit of phase decoherence time was estimated to be about 5 microseconds.

Aharonov-Casher-effect suppression of macroscopic tunneling of magnetic flux

We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf SQUID with the Josephson junction replaced by a Bloch transistor--two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q = e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.

Pinch resonances in a radio-frequency-driven superconducting-quantum-interference-device ring-resonator system

In this paper we present experimental data on the frequency domain response of a superconducting-quantum-interference-device ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency tank circuit resonator. We show that with the ring weakly hysteretic the resonance line shape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off line shapes exist as solutions of the nonlinear equations of motion for the system.

Quantum superposition of macroscopic persistent-current states

Microwave spectroscopy experiments have been performed on two quantum levels of a macroscopic superconducting loop with three Josephson junctions. Level repulsion of the ground state and first excited state is found where two classical persistent-current states with opposite polarity are degenerate, indicating symmetric and antisymmetric quantum superpositions of macroscopic states. The two classical states have persistent currents of 0.5 microampere and correspond to the center-of-mass motion of millions of Cooper pairs.

Strong coupling theory for driven tunneling and vibrational relaxation

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled non-Markovian master equations. We present analytical treatments that describe the dynamics in the regime of strong system-bath coupling. Our findings are corroborated by "ab initio" real-time path integral calculations.

Quantum superposition of distinct macroscopic states

In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.

Observation of cascaded two-photon-induced transitions between fluxoid states of a SQUID

We present evidence for transitions between fluxoid wells of a SQUID due to cascaded, two-photon processes. Such transitions are evidenced by an anomalous dependence on the transition rate from the one-photon resonant level within the initial well, which cannot be explained by previously observed macroscopic resonant tunneling. These two-photon processes may be a significant source of decoherence in SQUID qubits subject to microwave radiation.

Josephson persistent-current qubit

A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.