Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly-coupled Bose gas at a low temperature $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$-dependence of the rate is given mainly by $\exp(-c_s P/ 2T)$, where $P$ is the momentum transfer, and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate, compared to the non-uniform case. As a part of our calculation, we identify a complex instanton, whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.Comment: 15 pages, 3 figures; to be published in Phys. Rev.

Statistics and noise in a quantum measurement process

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and expect this description to apply for a wide class of quantum measurements. We derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum.Comment: 4 pages, 2 figure

Scenario for Ultrarelativistic Nuclear Collisions: Space--Time Picture of Quantum Fluctuations and the Birth of QGP

We study the dynamics of quantum fluctuations which take place at the earliest stage of high-energy processes and the conditions under which the data from e-p deep-inelastic scattering may serve as an input for computing the initial data for heavy-ion collisions at high energies. Our method is essentially based on the space-time picture of these seemingly different phenomena. We prove that the ultra-violet renormalization of the virtual loops does not bring any scale into the problem. The scale appears only in connection with the collinear cut-off in the evolution equations and is defined by the physical properties of the final state. In heavy-ion collisions the basic screening effect is due to the mass of the collective modes (plasmons) in the dense non-equilibrium quark-gluon system, which is estimated. We avoid the standard parton phenomenology and suggest a dedicated class of evolution equations which describe the dynamics of quantum fluctuations in heavy-ion collisions.Comment: 54 pages, 11 Postscript figures, uses RevTe

Full Frequency Back-Action Spectrum of a Single Electron Transistor during Qubit read-out

We calculate the spectral density of voltage fluctuations in a Single Electron Transistor (SET), biased to operate in a transport mode where tunneling events are correlated due to Coulomb interaction. The whole spectrum from low frequency shot noise to quantum noise at frequencies comparable to the SET charging energy $(E_{C}/\hbar)$ is considered. We discuss the back-action during read-out of a charge qubit and conclude that single-shot read-out is possible using the Radio-Frequency SET.Comment: 4 pages, 5 figures, submitted to PR

Nondemolition measurements of a single quantum spin using Josephson oscillations

We consider a Josephson junction containing a single localized spin 1/2 between conventional singlet superconducting electrodes. We study the spin dynamics and measurements when a dc-magnetic field ${\bf B}\parallel z$ acts on the spin and the junction is embedded into a dissipative circuit. We show that when tunneling or a voltage are turned on at time $t=0$ the Josephson current starts to oscillate with an amplitude depending on the initial ($t=0$) value of the spin $z$-component, $S_z= \pm 1/2$. At low temperatures, when effects of quasiparticles may be neglected, this procedure realizes a quantum-non-demolition (QND) measurement of $S_z$.Comment: 4 pages, 1 figure; average value of spin z operator changed to eigenvalue S_

Spectral Flow, Magnus Force and Mutual Friction via the Geometric Optics Limit of Andreev Reflection

The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasiparticles --- thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillations which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients.Comment: Plain TeX, 19 pages, 5 encapsulated postscript figure

On local invariants of pure three-qubit states

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree less than or equal to 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio

Spin and Current Variations in Josephson Junctions

We study the dynamics of a single spin embedded in the tunneling barrier between two superconductors. As a consequence of pair correlations in the superconducting state, the spin displays rich and unusual dynamics. To properly describe the time evolution of the spin we derive the effective Keldysh action for the spin. The superconducting correlations lead to an effective spin action, which is non-local in time, leading to unconventional precession. We further illustrate how the current is modulated by this novel spin dynamics

Quantum dynamics of a model for two Josephson-coupled Bose--Einstein condensates

In this work we investigate the quantum dynamics of a model for two single-mode Bose--Einstein condensates which are coupled via Josephson tunneling. Using direct numerical diagonalisation of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalised and self-trapping phases. We show that these behaviours are dependent on both the initial state of the system as well as regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.Comment: 15 pages, 8 eps figures, accepted in J. Phys.