Sub-shot-noise phase sensitivity with a Bose-Einstein condensate Mach-Zehnder interferometer

Abstract

Bose Einstein Condensates, with their coherence properties, have attracted wide interest for their possible application to ultra precise interferometry and ultra weak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity ∆θ scaling with the total number of condensate particles N as i) the standard quantum limit ∆θ ∼ 1/N 1/2 , ii) the sub shot-noise ∆θ ∼ 1/N 3/4 and the iii) the Heisenberg limit ∆θ ∼ 1/N . However, in a realistic dynamical BEC splitting, the 1/N limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub shot-noise sensitivity ∆θ ∼ 1/N 3/4 can be reached in a realistic experimental setting. We also show that the 1/N 3/4 scaling is a rigorous upper bound in the limit N → ∞, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.PACS numbers:

Optimized Double-Well Quantum Interferometry with Gaussian Squeezed States

“…On the other hand, if holding u fixed so that N 1=4 , the phase uncertainty scales as 1=N 3=4 for 0, as discussed in Ref. [26], and would eventually saturate to 1= N p for Þ 0. Rather than holding or u fixed, we propose varying u and thus with N in order to minimize the phase variance.…”

Entanglement-enhanced atomic gyroscope

“…The use of numbersqueezed atomic states will allow for Heisenberg limited precisions and as such there has been much research into the generation and uses of these squeezed states [7][8][9][10]. Several proposals have already been made to use these squeezed, and other entangled atomic states, such as maximally entangled "NOON" (|N, 0 > +|0, N >) states, to make general phase measurements with sub-shot-noise sensitivities [11][12][13][14][15][16][17]. It has also been shown that uncorrelated atoms can also achieve sub-shot-noise sensitivities of rotational phase shifts [18] by using a chain of matter wave interferometers or a chain of gyroscopes.…”

Multipartite-entanglement tomography of a quantum simulator

“…The investigation of ME in the ground state of the Ising chains, as witnessed by the QFI and the WSS, has been limited so far to the two extreme cases of nearest-neighbor a = ¥ [48,49,96] and infinite-range 0 a = interaction [47,96]. Several works have analyzed the QFI and the WSS in the ground state of the bosonic Josephson junction, which formally corresponds to the fully connected Ising model restricted to the Hilbert subspace of states that are symmetric under particle exchange [41,49,97]: see [41,[98][99][100] for experimental investigations in Bose-Einstein condensates. Notice that the ground state of the Hamiltonian(1) for α=0 is indeed given by symmetric states.…”