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Journal of Physics B Atomic Molecular and Optical Physics

Dephasing of entangled atoms as an improved test of quantized space time

Mark S. Everitt, Martin L. Jones, Benjamin T. H. Varcoe

Published Nov 7, 2013• 5 citations
Publisher

Abstract

Cavity quantum electrodynamics (QED) has been highly successful in the demonstration of many features of quantum mechanics and in this paper we introduce a potential future application of cavity QED to the detection of quantized space time. Wang et al (2006 Class. Quantum Grav. 23 L59), demonstrated that the phase of a particle fluctuated due to interactions with random deviations of a conformal gravitational field and therefore that atom interferometers may be sensitive to these fluctuations. Hence, it is possible that sensitivity to Planck scale effects could be achieved with a sufficiently sensitive interferometer. In this paper we demonstrate that a class of entangled states, the N -atom Greenberger–Horne–Zeilinger states, provide a better scaling than atom interferometry and that current experiments are capable of making a significant impact in this field. We outline an experiment which uses atomic beams of rubidium atoms excited to Rydberg states that undergo controlled collisions in high- Q microwave resonators in a sequence that makes the resulting state highly sensitive to conformal field fluctuations. We show that a significant advance in sensitivity is possible.

DOI
10.1088/0953-4075/46/22/224003

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Cavity quantum electrodynamics (QED) has been highly successful in the demonstration of many features of quantum mechanics and in this paper we introduce a potential future application of cavity QED to the detection of quantized space time. Wang et al (2006 Class. Quantum Grav. 23 L59), demonstrated that the phase of a particle fluctuated due to interactions with random deviations of a conformal gravitational field and therefore that atom interferometers may be sensitive to these fluctuations. Hence, it is possible that sensitivity to Planck scale effects could be achieved with a sufficiently sensitive interferometer. In this paper we demonstrate that a class of entangled states, the N -atom Greenberger–Horne–Zeilinger states, provide a better scaling than atom interferometry and that current experiments are capable of making a significant impact in this field. We outline an experiment which uses atomic beams of rubidium atoms excited to Rydberg states that undergo controlled collisions in high- Q microwave resonators in a sequence that makes the resulting state highly sensitive to conformal field fluctuations. We show that a significant advance in sensitivity is possible.
In a recent article Wang et al. (Class. Quantum Grav. 23 (2006) L59), demonstrated that the phase of a particle fluctuates due to interactions with random deviations of a conformal gravitational field. Furthermore they demonstrated that atom interferometers are sensitive to these fluctuations and that sensitivity to Planck scale effects could be achieved with a sufficiently sensitive interferometer. In this paper we demonstrate that a class of entangled states, the N-atom Greenberger-Horne-Zeilinger (GHZ) states, provide a better scaling than atom interferometers and that current experiments are capable of making a significant impact in this field. We outline an experiment which uses atomic beams of rubidium atoms excited to Rydberg states. The atoms undergo controlled collisions in high quality factor microwave resonators in a sequence that makes the resulting state highly sensitive to conformal field fluctuations. We show that a significant advance in sensitivity is possible.
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+1.13\,.\,{4}_{-0.9}^{+1.1}3.4−0.9+1.1​ 3 . 4 − 0.9 + 1.1 dB and 2 . 5−0.6+0.62\,.\,{5}_{-0.6}^{+0.6}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+0.51\,.\,{7}_{-0.5}^{+0.5}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 .
An alternative scheme is presented for teleportation of a two-atom entangled state in cavity quantum electrodynamics (QED). It is based on the resonant atom–cavity field interaction. In the scheme, only one cavity is involved, and the number of the atoms needed to be detected is decreased compared with the previous scheme. Since the resonant atom–cavity field interaction greatly reduces the interaction time, the decoherence effect can be effectively suppressed during the teleportation process. The experimental feasibility of the scheme is discussed. The scheme can easily be generalized to the teleportation of N-atom Greeninger–Horne–Zeilinger (GHZ) entangled states. The number of atoms needed to be detected does not increase as the number of the atoms in the GHZ state increases.
We propose a Ramsey interferometry experiment using an entangled state of N atoms to approach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with a state of art apparatus.
We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with state of art apparatuses. 1
We present the experimental realisation of a cavity QED atom interferometer based on two consecutive resonant interactions of a circular Rydberg atom with the field mode of a high Q microwave resonator that is initially prepared in the vacuum state. The interferometer scheme is analogous to the Ramsey method with the classical field replaced by the quantum field stored in the cavity mode. We demonstrate the possibility to use this technique to probe, by dispersive interaction, the field stored in a second mode of the resonator.