We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. [Phys. Rev. Lett. 104, 200402 (2010)] is used to generate subshotnoise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilizing all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.
We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. [Phys. Rev. Lett. 104, 200402 (2010)] is used to generate subshotnoise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilizing all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.
Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].
Abstract An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit 1–3 set by projections of individual atoms. Large amounts of entanglement 4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles 4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity 3.4−0.9+1.1 3 . 4 − 0.9 + 1.1 dB and 2.5−0.6+0.6 2 . 5 − 0.6 + 0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity 1.7−0.5+0.5 1 . 7 − 0.5 + 0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors 17,18 , searches for new physics, particles and fields 19–23 , future advanced gravitational wave detectors 24,25 and accessing beyond mean-field quantum many-body physics 26–30 .
We have developed an atom interferometer to observe two-atom interference of a momentum entangled state. The setup is similar to one used recently in our laboratory to observe the Hong Ou Mandel (HOM) effect for atoms [1], but instead of using two input and two output modes on a beam splitter, we use four input and four output modes. A diagram is shown below. The configuration is essentially that proposed in Ref. [2]. We observe correlations consistent with the presence of an entangled state. An improved setup will allow a test Bell’s inequalities for mechanical degrees of freedom of massive particles.[1] R. Lopes, et al., Nature 520, 66 (2015).[2] M. Horne, A. Shimony, and A. Zeilinger, Phys. Rev. Lett. 62, 2495 (1989).
We analyze methods designed to go beyond the standard quantum limit for a class of atomic interferometers, where the quantity of interest is the difference of phase shifts obtained by two independent atomic ensembles. An example is given by an atomic Sagnac interferometer, where for two ensembles propagating in opposite directions in the interferometer this phase difference encodes the angular velocity of the experimental setup. We discuss methods of separately or jointly squeezing observables of the two atomic ensembles, and compare in detail the advantages and drawbacks of such schemes. In particular, we show that the method of joint squeezing may improve the variance by up to a factor of 2. We take into account fluctuations of the number of atoms in both the preparation and the measurement stage, and obtain bounds on the difference between the numbers of atoms in the two ensembles, as well as on the detection efficiency, which have to be fulfilled in order to surpass the standard quantum limit. Under realistic conditions, the performance of both schemes can be improved significantly by reading out the phase difference via a quantum nondemolition measurement. Finally, we discuss a scheme using macroscopically entangled ensembles.
We investigate the prospect of enhancing the phase sensitivity of atom interferometers in the Mach-Zehnder configuration with squeezed light. Ultimately, this enhancement is achieved by transferring the quantum state of squeezed light to one or more of the atomic input beams, thereby allowing operation below the standard quantum limit. We analyze in detail three specific schemes that utilize (1) single-mode squeezed optical vacuum (i.e., low-frequency squeezing), (2) two-mode squeezed optical vacuum (i.e., high-frequency squeezing) transferred to both atomic inputs, and (3) two-mode squeezed optical vacuum transferred to a single atomic input. Crucially, our analysis considers incomplete quantum state transfer (QST) between the optical and atomic modes, and the effects of depleting the initially prepared atomic source. Unsurprisingly, incomplete QST degrades the sensitivity in all three schemes. We show that by measuring the transmitted photons and using information recycling [Phys. Rev. Lett. 110, 053002 (2013)], the degrading effects of incomplete QST on the sensitivity can be substantially reduced. In particular, information recycling allows scheme (2) to operate at the Heisenberg limit irrespective of the QST efficiency, even when depletion is significant. Although we concentrate on Bose-condensed atomic systems, our scheme is equally applicable to ultracold thermal vapors.
We theoretically investigate the generation of atom-light entanglement via Raman superradiance in an optical cavity, and show how this can be used to enhance the sensitivity of atom interferometry. We model a realistic optical cavity, and show that by careful temporal shaping of the optical local oscillator used to measure the light emitted from the cavity, information in the optical mode can be combined with the signal from the atom interferometer to reduce the quantum noise, and thus increase the sensitivity. It was found in Phys. Rev. Lett. 110, 053002 (2013) that an atomic ``seed'' was required in order to reduce spontaneous emission and allow for single mode behavior of the device. In this paper we find that the optical cavity reduces the need for an atomic seed, which allows for stronger atom-light correlations and a greater level of quantum enhancement.