Interferometric measurements with matter waves are established techniques for sensitive gravimetry, rotation sensing, and measurement of surface interactions, but compact interferometers will require techniques based on trapped geometries. In a step towards the realization of matter wave interferometers in toroidal geometries, we produce a large, smooth ring trap for Bose-Einstein condensates using rapidly scanned time-averaged dipole potentials. The trap potential is smoothed by using the atom distribution as input to an optical intensity correction algorithm. Smooth rings with a diameter up to 300 µm are demonstrated. We experimentally observe and simulate the dispersion of condensed atoms in the resulting potential, with good agreement serving as an indication of trap smoothness. Under time of flight expansion we observe low energy excitations in the ring, which serves to constrain the lower frequency limit of the scanned potential technique. The resulting ring potential will have applications as a waveguide for atom interferometry and studies of superfluidity.Submitted to: New J. Phys. arXiv:1512.05079v4 [cond-mat.quant-gas]
Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor BoseEinstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU (1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particleresolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.
Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cramér-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.Nonclassical states enable precision measurements below the shot-noise limit (SNL) [1, 2]. However, despite many proof-of-principle experiments [3][4][5][6][7], a useful (i.e., highprecision) quantum-enhanced measurement has yet to be performed. This is partially due to the fragility of nonclassical states to typical noise sources [8] and the difficulty in marrying quantum-state-generation protocols with the practical requirements of high-precision metrology [9,10]; addressing these issues is an active research area [11][12][13][14][15][16][17][18]. A key limitation is detection noise [7,[19][20][21][22][23][24][25], which makes n and n ± σ particles indistinguishable. Quantum-enhanced measurements typically require single-particle resolution (σ ∼ 1), which restricts them to small particle numbers, since the requisite counting efficiency rapidly becomes unattainable as particle number increases.Another challenge is that many protocols are suboptimal, as they do not fully exploit the state's quantum correlations. Specifically, an estimate of classical parameter φ obtained from measurement signalŜ has a precision ∆φ2 . A quantum-enhanced estimate surpasses the SNL ∆φ 2 = 1/N for particle number N , however it is only optimal if it saturates the quantum Cramér-Rao bound (QCRB) ∆φ 2 = 1/F Q , where F Q is the quantum Fisher information (QFI) [8,[26][27][28]. For example, consider the nonclassical N -qubit states generated via the one-axis twisting (OAT) Hamiltonian [29][30][31][32]. Typical spin-squeezing procedures use the expectation of pseudospin as the signal, yielding a minimuim sensitivity ∆φ 2 ∼ N −5/3 . However, OAT can produce entangled non-Gaussian states (ENGS), which can achieve the Heisenberg limit (HL) F Q = N 2 and the...
We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive blue-detuned light barrier, intersecting the BoseEinstein condensate, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the wave front splits into two parts and clear fringes appear. The experiment is modeled using an effective one-dimensional Gross-Pitaevskiilike equation and gives excellent quantitative agreement with the experiment, even though matter waves with wavelengths two orders of magnitude smaller than the healing length are present. In these experiments, no significant heating or particle loss is observed.
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