Optimized Double-Well Quantum Interferometry with Gaussian Squeezed States

Huang, Yu Ping; Moore, Michael

doi:10.1103/physrevlett.100.250406

Cited by 36 publications

(43 citation statements)

References 28 publications

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“…Current research on linear interferometers is directed at the search for optimal input states and output measurements [2][3][4][5][6][7][8][9][10][11][12], adaptive phase measurement schemes [13][14][15][16], and the influence of particle losses [17][18][19]. Several proof-ofprinciple experiments reaching a sub shot-noise sensitivity have been performed, for a fixed number of particles with photons [20][21][22][23][24] and ions [25], while squeezed states for interferometry with a non-fixed number of particles have been prepared with Bose-Einstein-condensates [26][27][28][29][30], atoms at room temperature [31] and light [32,33].…”

Section: Introductionmentioning

confidence: 99%

Not all pure entangled states are useful for sub-shot-noise interferometry

2010

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We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of N particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for N = 2 all pure entangled states can be made useful for sub shot-noise interferometry while for N > 2 this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.

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Section: Introductionmentioning

confidence: 99%

Not all pure entangled states are useful for sub-shot-noise interferometry

2010

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“…As in our analysis of the MZ interferometer [13,14], this propagator acts on a Gaussian squeezed state, of the form,…”

Section: Measurement Scheme and Optimization Proceduresmentioning

confidence: 99%

“…In previous work [13,14], we have carried out such optimization for Gaussian Squeezed States (GSS), which constitute an excellent approximation to the ground-state of the bimodal BEC at T=0, with the squeezing controlled by adiabatic variation of the interaction-to-tunneling ratio [15]. The GSS also closely approximates the states formed dynamically by the nonlinear beam-splitting of Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Using this approach, we found that the optimal preparation changes from a number-squeezed state (transformed to hold-time phase-squeezed state by the beamsplitter) with σ o ∼ N 1/3 in the absence of interactions [13] to a phase-squeezed state with σ o ∼ √ ηN (here and below 'o' subscripts indicate optimal values) for strong interactions [14]. The resulting optimal SNR is subject to a similar transition from the better than shotnoise scaling s o ∼ N 2/3 without interactions to the strong-interaction behavior of s o ∼ N/η.…”

Section: Introductionmentioning

confidence: 99%

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Robust sub-shot-noise measurement via Rabi-Josephson oscillations in bimodal Bose-Einstein condensates

2011

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Mach-Zehnder atom interferometry requires hold-time phase-squeezing to attain readout accuracy below the standard quantum limit. This increases its sensitivity to phase-diffusion, restoring shot-noise scaling of the optimal signal-to-noise ratio, so, in the presence of interactions. The contradiction between the preparations required for readout accuracy and robustness to interactions, is removed by monitoring Rabi-Josephson oscillations instead of relative-phase oscillations during signal acquisition. Optimizing so with a Gaussian squeezed input, we find that hold-time number squeezing satisfies both demands and that sub-shot-noise scaling is retained even for strong interactions.

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“…Interferometers with trapped ultra-cold atoms are valuable tools for the precise measurement of external forces [1]. A promising one is the double-well Mach-Zehnder interferometer (MZI) [2,3,4,5,6,7,8]. This requires two 50/50 beam splitters implemented by a dynamical manipulation of the inter-well barrier.…”

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confidence: 99%

Rabi interferometry and sensitive measurement of the Casimir-Polder force with ultracold gases

et al. 2010

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We show that Rabi oscillations of a degenerate fermionic or bosonic gas trapped in a double-well potential can be exploited for the interferometric measurement of external forces at micrometer length scales. The Rabi interferometer is less sensitive, but easier to implement, than the MachZehnder since it does not require dynamical beam-splitting/recombination processes. As an application we propose a measurement of the Casimir-Polder force acting between the atoms and a dielectric surface. We find that even if the interferometer is fed with a coherent state of relatively small number of atoms, and in the presence of realistic experimental noise, the force can be measured with a sensitivity sufficient to discriminate between thermal and zero-temperature regimes of the Casimir-Polder potential. Higher sensitivities can be reached with spin squeezed states. Introduction. Interferometers with trapped ultra-cold atoms are valuable tools for the precise measurement of external forces [1]. A promising one is the double-well Mach-Zehnder interferometer (MZI) [2,3,4,5,6,7,8]. This requires two 50/50 beam splitters implemented by a dynamical manipulation of the inter-well barrier. The phase shift is accumulated during the interaction of atoms with an external potential in the absence of the inter-well coupling. It is interesting to search for alternative interferometric schemes which can be easier to realize and therefore can be more stable than the MZI. In this Letter we propose a new protocol to create a Rabi interferometer. It can be implemented using either degenerate spin-polarized Fermions or non-interacting Bose-Einstein condensates (BECs) trapped in a double-well potential. The gas tunnels between the two wells while acquiring, at the same time, a phase shift. The relative number of particles among the two wells undergoes Rabi oscillations analogous to those experienced by a collection of two-level atoms in a radio frequency field [9]. The measurement of population imbalance as a function of time allows to infer the value of the external force as it affects both the amplitude and frequency of Rabi oscillations. The Rabi interferometer is less sensitive than the MZI, but does not require any splitting/recombination processes and is suitable for the estimation of forces rapidly decaying with distance. In particular, once fed with a fermionic/bosonic spin coherent state, the interferometer allows for the accurate measurement of the CasimirPolder force between the atomic sample and a surface. We show that even in the presence of typical experimental noise it is possible to distinguish between thermal and zero-temperature regimes of the Casimir-Polder potential [10], which has not yet been achieved in experiment [11,12,13,14,15]. Moreover, we demonstrate that the Rabi interferometer can further benefit from the use of entangled states as input. In analogy to the MZI, a sub shot-noise phase sensitivity can be obtained with spin squeezed states recently created with a BEC [16].The Rabi interferometer. Let us consider a d...

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Optimized Double-Well Quantum Interferometry with Gaussian Squeezed States

Cited by 36 publications

References 28 publications

Not all pure entangled states are useful for sub-shot-noise interferometry

Not all pure entangled states are useful for sub-shot-noise interferometry

Robust sub-shot-noise measurement via Rabi-Josephson oscillations in bimodal Bose-Einstein condensates

Rabi interferometry and sensitive measurement of the Casimir-Polder force with ultracold gases

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