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arXiv:1511.03893

Adiabatic Mach-Zehnder interferometer in dipolar spin-1 condensate

Yixiao Huang, Wei Guo, Ning-Ju Hui, Zheng-Da Hu

Published Nov 12, 2015• 0 citations
arXivHTMLPDF

Abstract

Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also discuss the spin-$1$ squeezing induced in the adiabatic passage and show that the squeezing parameter attains its minimal value near the point of saturation field.

DOI
10.48550/arxiv.1511.03893

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Mach-Zehnder interferometer, a powerful tool for a wide variety of measurements, has been realized with Bose-Einstein condensates in recent experiments. In this report, we propose and analyze a realizable scheme for performing a Heisenberg-limited Mach-Zehnder interferometry with dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach-Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also discuss the spin-111 squeezing induced in the adiabatic passage and show that the squeezing parameter attains its minimal value near the point of saturation field.
We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson junction with a negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.
We theoretically analyze a Mach-Zehnder interferometer with trapped condensates and find that it is surprisingly stable against the nonlinearity induced by interparticle interactions. The phase sensitivity, which we study for number-squeezed input states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or maximum-likelihood phase estimation strategy is used. We finally demonstrate the robustness of the Mach-Zehnder interferometer in the presence of interactions against condensate oscillations and a realistic atom-counting error.
Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach–Zehnder sequence with trapped Bose–Einstein condensates confined on an atom chip. Particle interactions in our Bose–Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors. Atom interferometers exploit wave-particle duality and can be used as sensitive measurement devices. Berrada et al.present a Mach–Zehnder interferometer for Bose–Einstein condensates trapped on an atom chip and demonstrate enhanced performance using non-classical states.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.
Bose-Einstein condensates (BEC), with their coherence properties, have attracted wide interest for their possible application to ultraprecise interferometry and ultraweak 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 $\ensuremath{\Delta}\ensuremath{\theta}$ scaling with the total number of condensate particles NNN as (i) the standard quantum limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{1∕2}$, (ii) the sub shot-noise $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$, and the (iii) the Heisenberg limit $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕N$. However, in a realistic dynamical BEC splitting, the 1∕N1∕N1∕N limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub-shot-noise sensitivity $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}1∕{N}^{3∕4}$ can be reached in a realistic experimental setting. We also show that the 1∕N3∕41∕{N}^{3∕4}1∕N3∕4 scaling is a rigorous upper bound in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.
We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of NNN atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.