Phase oscillations in superfluid 3He-B weak links

Oscillations in quantum phase about a mean value of $\pi$, observed across micropores connecting two \helium baths, are explained in a Ginzburg-Landau phenomenology. The dynamics arises from the Josephson phase relation,the interbath continuity equation, and helium boundary conditions. The pores are shown to act as Josephson tunnel junctions, and the dynamic variables are the inter bath phase difference and fractional difference in superfluid density at micropores. The system maps onto a non-rigid, momentum-shortened pendulum, with inverted-orientation oscillations about a vertical tilt angle $\phi = \pi$, and other modes are predicted

Instability of the superfluid flow as black-hole lasing effect

We show that the instability leading to the decay of the one-dimensional superfluid flow through a penetrable barrier are due to the black-hole lasing effect. This dynamical instability is triggered by modes resonating in an effective cavity formed by two horizons enclosing the barrier. The location of the horizons is set by $v(x)=c(x)$, with $v(x),c(x)$ being the local fluid velocity and sound speed, respectively. We compute the critical velocity analytically and show that it is univocally determined by the horizons configuration. In the limit of broad barriers, the continuous spectrum at the origin of the Hawking-like radiation and of the Landau energetic instability is recovered.Comment: 18 pages, 3 figure

Phase Estimation With Interfering Bose-Condensed Atomic Clouds

We investigate how to estimate from atom-position measurements the relative phase of two Bose-Einstein condensates released from a double-well potential. We demonstrate that the phase estimation sensitivity via the fit of the average density to the interference pattern is fundamentally bounded by shot noise. This bound can be overcome by estimating the phase from the measurement of $\sqrt N$ (or higher) correlation function. The optimal estimation strategy requires the measurement of the $N$-th order correlation function. We also demonstrate that a second estimation method -- based on the detection of the center of mass of the interference pattern -- provides sub shot-noise sensitivity. Yet, the implementation of both protocols might be experimentally challenging.Comment: 4 pages, 2 figure

Staying adiabatic with unknown energy gap

We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total evolution time. We test the algorithm on the Landau-Zener transition and then apply it on the quantum adiabatic computation of 3-SAT: The result is compatible with an exponential speed-up for up to twenty qubits with respect to classical algorithms. We finally study a possible algorithm improvement by combining it with the quantum Zeno effect.Comment: 4 pages, 4 figure

Phase Estimation from Atom Position Measurements

We study the measurement of the position of atoms as a means to estimate the relative phase between two Bose-Einstein condensates. First, we consider $N$ atoms released from a double-well trap, forming an interference pattern, and show that a simple least-squares fit to the density gives a shot-noise limited sensitivity. The shot-noise limit can instead be overcome by using correlation functions of order $\sqrt{N}$ or larger. The measurement of the $N\mathrm{th}$-order correlation function allows to estimate the relative phase at the Heisenberg limit. Phase estimation through the measurement of the center-of-mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of the overlap between the two clouds on the phase estimation, when Mach-Zehnder interferometry is performed in a double-well.Comment: 20 pages, 6 figure

Mach-Zehnder interferometry with interacting trapped Bose-Einstein condensates

We theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.Comment: 4 pages, 5 figures, minor revision

Entanglement, Non-linear Dynamics, and the Heisenberg Limit

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.Comment: Phys. Rev. Lett. 102, 100401 (2009