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arXiv:2202.05763 · Physical Review Research

Light-pulse atom interferometry with entangled atom-optical elements

Tobias Asano, Fabio Di Pumpo, Enno Giese

Published Feb 11, 2022• 1 citation
arXivHTMLPDF

Abstract

The analogs of optical elements in light-pulse atom interferometers are generated from the interaction of matter waves with light fields. As such, these fields possess quantum properties, which fundamentally lead to a reduced visibility in the observed interference. This loss is a consequence of the encoded information about the atom's path. However, the quantum nature of the atom-optical elements also gives an additional degree of freedom to reduce such effects: We demonstrate that entanglement between all light fields can be used to erase information about the atom's path and by that to partially recover the visibility. Thus, our work highlights the role of complementarity on atom-interferometric experiments.

DOI
10.1103/physrevresearch.4.013115

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The analogs of optical elements in light-pulse atom interferometers are generated from the interaction of matter waves with light fields. As such, these fields possess quantum properties, which fundamentally lead to a reduced visibility in the observed interference. This loss is a consequence of the encoded information about the atom's path. However, the quantum nature of the atom-optical elements also gives an additional degree of freedom to reduce such effects: We demonstrate that entanglement between all light fields can be used to erase information about the atom's path and by that to partially recover the visibility. Thus, our work highlights the role of complementarity on atom-interferometric experiments.
The far-field patterns of atoms diffracted from a classical light field or from a quantum one in a photon-number state are identical. On the other hand, diffraction from a field in a coherent state, which shares many properties with classical light, displays a completely different behavior. We show that in contrast to the diffraction patterns, the interference signal of an atom interferometer with light-pulse beam splitters and mirrors in intense coherent states does approach the limit of classical fields. However, low photon numbers reveal the granular structure of light, leading to a reduced visibility since welcher-Weg (which-way) information is encoded into the field. We discuss this effect for a single photon-number state as well as a superposition of two such states.
The far-field patterns of atoms diffracted from a classical light field or from a quantum one in a photon-number state are identical. On the other hand, diffraction from a field in a coherent state, which shares many properties with classical light, displays a completely different behavior. We show that in contrast to the diffraction patterns, the interference signal of an atom interferometer with light-pulse beam splitters and mirrors in intense coherent states does approach the limit of classical fields. However, low photon numbers reveal the granular structure of light, leading to a reduced visibility since welcher-Weg (which-way) information is encoded into the field. We discuss this effect for a single photon-number state as well as a superposition of two such states.
A quantum eraser is proposed that operates in a domain that does not have any classical counterpart. This quantum eraser utilizes the complementary aspect between entanglement and single-partite properties of composite quantum systems. Consequently, in contrast to the duality of visibility and which-path information which establish features of single quantum systems, here, properties of composite quantum systems are considered. In composite quantum systems entanglement might emerge which is of genuine quantum origin. This nonclassical correlation mutually exclude the single-partite properties of the subsystems of the composite quantum system. The single-partite properties can be describes by wave- and particle properties, i.e. the standard wave-particle duality. Remarkably, entanglement can be considered as a resource for observables that do not exist in classical physics. In a bipartite photon system, this observable is the two-particle visibility which describes the phase relations that are shared between both photons of the composite system. The complementary aspect between two-particle visibility and single-partite properties of the subsystems prevents us from the observation of single-partite properties in an entangled biphoton system. The quantum eraser erases the two-partite visibility and retrieves single-partite properties in form of single-particle visibility for both of the two photons. Thus, both observables contain phase information giving rise to interference effects. Here, complementarity is explicitly enforced by entanglement in a quantitative manner.
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 .
The wave nature of particles has been demonstrated in many experiments and it continues to be an active area of research [1]. Optical elements for atoms such as beam splitters and mirrors have been used for the manipulation of atomic deBroglie waves. Many of these elements use light forces which under certain conditions allow the coherent manipulation of the atoms and thus are important for atom interferometry. Atom interferometers have many uses, including the precise measurement of fundamental constants.
Two-path complementarity in polarized interferometric fields is reconsidered by retaining the complete path--polarization density matrix instead of reducing the description to the path degree of freedom from the outset. The familiar relation connecting the Cartesian visibility components, path predictability, and reduced-state mixedness is recovered as a marginal consequence of the reduced path state and is not interpreted as a new complementarity law. Attention is focused instead on the full path--polarization description in a real reference basis adapted to the path and linear-polarization degrees of freedom. Within this framework, the normalized purity separates naturally into path, polarization, and path--polarization-correlation contributions, while the antisymmetric sector provides a sector-resolved measure of cohesion. The resulting decomposition identifies which parts of the complete state store phase-sensitive interferometric coherence and which contributions are removed when polarization is traced out. The formalism therefore provides a sector-resolved accounting of complementarity within the full path--polarization state and clarifies the connection between reduced visibility loss, polarization marking, path--polarization correlations, and quantum-eraser recovery. The present article establishes the framework and associated purity decomposition; a more detailed exploration of full path--polarization complementarity and its dynamical aspects is left for future work.