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arXiv:cond-mat/0511234 · Physical Review A

Cavity QED detection of interfering matter waves

Thomas Bourdel, Tobias Donner, Stephan Ritter, Anton Öttl, Michael Köhl, Tilman Esslinger

Published Apr 5, 2006• 38 citations
arXivHTMLPDF

Abstract

We observe the build-up of a matter wave interference pattern from single atom detection events in a double-slit experiment. The interference arises from two overlapping atom laser beams extracted from a rubidium Bose-Einstein condensate. Our detector is a high-finesse optical cavity which realizes a quantum measurement of the presence of an atom and thereby projects delocalized atoms into a state with zero or one atom in the resonator. The experiment reveals simultaneously the granular and the wave nature of matter. We present a setup which is suited for applications in atom interferometry and cavity QED.

DOI
10.1103/physreva.73.043602

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We observe the build-up of a matter wave interference pattern from single atom detection events in a double-slit experiment. The interference arises from two overlapping atom laser beams extracted from a rubidium Bose-Einstein condensate. Our detector is a high-finesse optical cavity which realizes a quantum measurement of the presence of an atom and thereby projects delocalized atoms into a state with zero or one atom in the resonator. The experiment reveals simultaneously the granular and the wave nature of matter. We present a setup which is suited for applications in atom interferometry and cavity QED.
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 double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern emerges after many discrete particle impacts as if each particle is passing through both slits and interfering with itself. Here we present a temporally- and spatially-resolved measurement of the double-slit interference pattern using single photons. We send single photons through a birefringent double-slit apparatus and use a linear array of single-photon detectors to observe the developing interference pattern. The analysis of the buildup allows us to compare quantum mechanics and the corpuscular model, which aims to explain the mystery of single-particle interference. Finally, we send one photon from an entangled pair through our double-slit setup and show the dependence of the resulting interference pattern on the twin photon's measured state. Our results provide new insight into the dynamics of the buildup process in the double-slit experiment, and can be used as a valuable resource in quantum information applications.
The experimental realization of Bose-Einstein condensates in dilute alkali gases has opened up the possibility to perform time and space domain interferometry with coherent matter waves. We have exploited different configurations realizing coherent matter wave interferometers: in a first set of exeperiments we create a twofold condensate sample investigating the interplay between internal and external degrees of freedom in the matter wave analogous of a Young diffraction experiment. In a second experimental arrangement we produce a one dimensional array of condensates in an optical lattice. Upon release from the optical lattice the condensates are made to interfere, the resulting interference pattern, this time analogous to an optical diffraction grating, is used to extract information about static and dynamical properties of the sample.
The phenomenon of matter-wave interference lies at the heart of quantum physics. It has been observed in various contexts in the limit of non-interacting particles as a single-particle effect. Here we observe and control matter-wave interference whose evolution is driven by interparticle interactions. In a multi-path matter-wave interferometer, the macroscopic many-body wave function of an interacting atomic Bose–Einstein condensate develops a regular interference pattern, allowing us to detect and directly visualize the effect of interaction-induced phase shifts. We demonstrate control over the phase evolution by inhibiting interaction-induced dephasing and by refocusing a dephased macroscopic matter wave in a spin-echo-type experiment. Our results show that interactions in a many-body system lead to a surprisingly coherent evolution, possibly enabling narrow-band and high-brightness matter-wave interferometers based on atom lasers.
This thesis features fundamental experiments on the coherence properties of Bose-Einstein condensates (BEC) and atom lasers, made possible by a newly developed apparatus combining a Bose-Einstein condensate with an ultrahigh nesse optical cavity.Using the cavity as a single atom detector, atoms extracted from a trapped cloud are detected with unprecedented sensitivity, and the rst time-resolved counting of single atoms from a quantum degenerate source was demonstrated.O-diagonal long-range order is a dening property of a BEC and equivalent to longrange phase coherence.Its formation is a complex process accompanied by spontaneous symmetry breaking.We witnessed this formation in an ultracold cloud of 87 Rb atoms crossing the phase transition of BEC.Two overlapping atomic beams originating from dierent positions inside the condensate propagated downwards into the cavity.They showed a matter wave interference pattern with a visibility determined by the coherence of the probed regions.The modulation of the ux of atoms, recorded with single-atom resolution, yields the visibility, whereas its mean value gives information about the density of the sample.By shock cooling, a cloud of atoms was prepared in a highly nonequilibrium state slightly above the phase transition.While the ensemble subsequently relaxed, it crossed the phase transition into an equilibrium with a small condensate fraction.Employing our minimally invasive measurement method, the growth of both the rst-order coherence and the density of the sample was tracked in real time while the system crossed the phase transition.The growth of the coherence was found to start later, proceed faster and nish earlier than the increase in density.The coherent region increased at one fth of the speed of sound.Employing time-resolved single atom counting with the cavity detector, the full counting statistics of an atom laser beam was recorded.In a Hanbury Brown and Twiss type experiment, the second-order correlation function was found to be constant g (2) (τ ) = 1.00±0.01,proving the atom laser's second-order coherence and the absence of excess intensity uctuations that were observed in a pseudothermal beam.An analysis of the time interval distributions of atoms in the beam conrmed these ndings.The iii
On the occasion of the hundredth anniversary of Albert Einstein's annus mirabilis , we reflect on the development and current state of research in cavity quantum electrodynamics in the optical domain. Cavity QED is a field which undeniably traces its origins to Einstein's seminal work on the statistical theory of light and the nature of its quantized interaction with matter. In this paper, we emphasize the development of techniques for the confinement of atoms strongly coupled to high-finesse resonators and the experiments which these techniques enable.