Interferometry below the standard quantum limit with Bose-Einstein condensates

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level

Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Robust quantum enhanced phase estimation in a multimode interferometer [corrected]

By exploiting the correlation properties of ultracold atoms in a multimode interferometer, we show how quantum enhanced measurement precision can be achieved with strong robustness to particle loss. While the potential for enhanced measurement precision is limited for even moderate loss in two-mode schemes, multimode schemes can be more robust. A ring interferometer for sensing rotational motion with noninteracting fermionic atoms can realize an uncertainty scaling of 1/(N√η) for N particles with a fraction η remaining after loss, which undercuts the shot-noise limit of two-mode interferometers. A second scheme with strongly interacting bosons achieves a comparable measurement precision and improved readout.

Real-world quantum sensors: evaluating resources for precision measurement

Quantum phenomena present in many experiments signify nonclassical behavior, but do not always imply superior performance. Quantifying the enhancement achieved from quantum behavior needs careful analysis of the resources involved. We analyze the case of parameter estimation using an optical interferometer, where increased precision can in principle be achieved using quantum probe states. Common performance measures are examined and some are shown to overestimate the improvement. For the simplest experimental case we compare the different measures and exhibit this overestimation explicitly. We give the preferred analysis of these experiments and calculate benchmark values for experimental parameters necessary to realize a precision enhancement. Our analysis shows that unambiguous real-world enhancements in optical quantum metrology with fixed photon number are yet to be attained.

Sub-poissonian number differences in four-wave mixing of matter waves

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub-shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests.

Quantum number theoretic transforms on multipartite finite systems

A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed.

Optimal quantum phase estimation

By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

Nonlocal quantum effects with Bose-Einstein condensates

We study theoretically the properties of two Bose-Einstein condensates in different spin states, represented by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions, giving access to the relative phase of the condensates. Initially, this phase is completely undefined, and the first measurements provide random results. But a fixed value of this phase rapidly emerges under the effect of the successive quantum measurements, giving rise to a quasiclassical situation where all spins have parallel transverse orientations. If the number of measurements reaches its maximum (the number of particles), quantum effects show up again, giving rise to violations of Bell type inequalities. The violation of Bell-Clauser-Horne-Shimony-Holt inequalities with an arbitrarily large number of spins may be comparable (or even equal) to that obtained with two spins.

Bose-Einstein condensates and precision measurements

An ongoing challenge in physics is to make increasingly accurate measurements of physical quantities. Bose-Einstein condensates in atomic gases are ideal candidates for use in precision measurement schemes since they are extremely cold and have laser-like coherence properties. In this paper, we review these two attributes and discuss how they could be exploited to improve the resolution in a range of different measurements.

Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice

We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.