Creation of macroscopic superpositions of flow states with Bose-Einstein condensates

We present a straightforward scheme for creating macroscopic superpositions of different superfluid flow states of Bose-Einstein condensates trapped in optical lattices. This scheme has the great advantage that all the techniques required are achievable with current experiments. Furthermore, the relative difficulty of creating cats scales favorably with the size of the cat. This means that this scheme may be well-suited to creating superpositions involving large numbers of particles. Such states may have interesting technological applications such as making quantum-limited measurements of angular momentum.Comment: 9 pages, 7 figure

Precision measurement with an optical Josephson junction

We study a new type of Josephson device, the so-called "optical Josephson junction" as proposed in Phys. Rev. Lett. {\bf 95}, 170402 (2005). Two condensates are optically coupled through a waveguide by a pair of Bragg beams. This optical Josephson junction is analogous to the usual Josephson junction of two condensates weakly coupled via tunneling. We discuss the use of this optical Josephson junction, for making precision measurements.Comment: 6 pages, 1 figur

Excitations of Bose-Einstein condensates in optical lattices

In this paper we examine the excitations observable in atoms confined in an optical lattice around the superfluid-insulator transition. We use increases in the number variance of atoms, subsequent to tilting the lattice as the primary diagnostic of excitations in the lattice. We show that this locally determined quantity should be a robust indicator of coherence changes in the atoms observed in recent experiments. This was found to hold for commensurate or non-commensurate fillings of the lattice, implying our results will hold for a wide range of physical cases. Our results are in good agreement with the quantitative factors of recent experiments. We do, howevers, find extra features in the excitation spectra. The variation of the spectra with the duration of the perturbation also turns out to be an interesting diagnostic of atom dynamics.Comment: 6 pages, 7 figures, using Revtex4; changes to version 2: new data and substantial revision of tex

Attaining subclassical metrology in lossy systems with entangled coherent states

Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust subclassical measurements [J. Joo et al., Phys. Rev. Lett. 107, 083601 (2011)]. Up to now no read-out scheme has been devised that exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss.We show substantial improvements over unentangled classical states and highly entangled NOON states for a wide range of loss values, elevating quantum metrology to a realizable technology in the near future

Effect of multimode entanglement on lossy optical quantum metrology

In optical interferometry multimode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false: single-mode quantum states perform just as well as their multimode entangled counterparts. We go beyond this to show that when photon losses occur, an inevitability in any realistic system, multimode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss. These results promote an alternate way of approaching optical quantum metrology using single-mode states that we expect to have great implications for the future

Control of the geometric phase and pseudo-spin dynamics on coupled Bose-Einstein condensates

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using the two-mode approach. Starting from Bloch states, we succeed to get analytical solutions for the TD Schroedinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differs by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one specie condensate in a double-well potential (external Josephson effect).Comment: 1 tex file and 11 figures in pdf forma

Efficient comparison of pathlengths using fourier multiport devices

Abstract We present a scheme for comparing effective path-lengths through a spatial region by using multipath generalizations of a Mach-Zehnder interferometer. This enables us to identify paths that have different lengths from the others with exponentially fewer measurements than would be required by repeated measurements with a standard two-path interferometer. We show that this scheme is extremely sensitive to small variations in the paths, which means it could be used to measure the variance of the path-lengths accurately and efficiently. Possible applications include accurately measuring spatial variations of potential fields and efficiently identifying which of many cavities contains an atom. The advent of interferometers allowed unprecedented levels of precision to be achieved in optical measurements. For the first time, path-length differences could be measured to within a small fraction of the wavelength, λ, of light. This dramatic improvement in resolution has kept interferometers at the forefront of a wide range of technological applications, particularly in the field of metrology. Ever since their inception, a great deal of effort has been devoted to enhancing the resolution of interferometers further still. One way this can be achieved is to use numbersqueezed light as the input [1-3]. For coherent light (i.e. light that is not squeezed), the path-length difference can be measured to within λ/ √ N , where N is the mean number of photons. By using perfectly number-squeezed light at the input, it is possible to substantially improve the resolution to λ/N. Another proposal for improving the resolution is to increase the number of paths through the interferometer. A standard Mach-Zehnder interferometer has two paths; by increasing this to d paths, the resolution scales as λ/(d √ N) In order to create multipath interferometers we need multiport generalizations of beam splitters. These multiport beam splitters are equivalent to so-called Fourier multiport devices, which relate the annihilation and creation operators at the output ports to those at the input ports through a finite Fourier transform. A significant body of work has been devoted t

Entanglement enhanced atomic gyroscope

The advent of increasingly precise gyroscopes has played a key role in the technological development of navigation systems. Ring-laser and fibre-optic gyroscopes, for example, are widely used in modern inertial guidance systems and rely on the interference of unentangled photons to measure mechanical rotation. The sensitivity of these devices scales with the number of particles used as $1/ \sqrt{N}$. Here we demonstrate how, by using sources of entangled particles, it is possible to do better and even achieve the ultimate limit allowed by quantum mechanics where the precision scales as 1/N. We propose a gyroscope scheme that uses ultra-cold atoms trapped in an optical ring potential.Comment: 19 pages, 2 figure