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Physical Review Letters

Loss of Spatial Coherence by a Single Spontaneous Emission

Tilman Pfau, Stefan J. Spalter, Christian Kurtsiefer, Christopher R. Ekstrom, J. Mlynek

Published Aug 29, 1994• 149 citations
Publisher

Abstract

We have demonstrated the loss of transverse spatial coherence of an atomic wave function after a single spontaneous emission. ${\mathrm{He}}^{*}$ atoms were both diffracted and excited by a standing light wave with a variable period. After the interaction, the excited atoms decay by a single spontaneously emitted photon. By changing the period of the standing light wave, we have mapped the loss of spatial coherence as a function of the transverse coordinate. By detecting the emitted photon one could "erase" the position information available and recover the transverse coherence in a correlation experiment, or realize a Heisenberg microscope.

DOI
10.1103/physrevlett.73.1223

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SPECTROSCOPIC TECHNIQUES FOR SINGLE ATOM LOCALIZATION

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Physical Review Letters•Aug 6, 2019•67 citations
We have demonstrated the loss of transverse spatial coherence of an atomic wave function after a single spontaneous emission. He∗{\mathrm{He}}^{*}He∗ atoms were both diffracted and excited by a standing light wave with a variable period. After the interaction, the excited atoms decay by a single spontaneously emitted photon. By changing the period of the standing light wave, we have mapped the loss of spatial coherence as a function of the transverse coordinate. By detecting the emitted photon one could "erase" the position information available and recover the transverse coherence in a correlation experiment, or realize a Heisenberg microscope.
We report a way of manipulating the spontaneous emission process leading to a spatial modulation of spontaneous decay. The effect is observed in the case of coherently driven atoms separated by less than a transition wavelength. It is quantified by Glauber's photon-photon second-order correlation function. We show that the photon arrival time, usually regarded as an entirely random process, depends not only on where a photon is detected but also on where a former photon had been recorded previously. Our results shed light on the unexpected consequences of state reduction and entanglement for the fundamental process of spontaneous emission.
We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time TTT to produce an echo signal at time 2T2T2T due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.
We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time TTT to produce an echo signal at time 2T2T2T due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.
Entanglement of the atom and field leads towards the measurement of the state of the atom or field depending on the kind of measurement made. Taking advantage of this fact, we propose spectroscopic methods for the single atom localization within the subwavelength domain of the optical standing wave field. \n \nWhen a two-level atom interacts with some intense radiation field the spectrum of the scattered light signal exhibits a three-peak Mollow spectrum. We propose a scheme of atom localization based on the resonance fluorescence from a two-level atom interacting with a standing wave field. The Rabi frequency is considered to be position dependent and therefore, the spontaneously emitted photon carries the information about the center-of-mass motion of the atom. This leads to the localization of the single atom by measuring the frequency of the spontaneously emitted photon even during the passage of the atom through the standing wave field. We predict a spatial resolution in position information of up to λ/60 where λ is the optical wavelength. \n \nDetuning of the coherent field with the atomic transition plays an important role in the characterization of the peaks present in the Autler- Townes spectrum of a three-level atom. Strong line narrowing is observed in one of the peaks of the Autler- Townes doublet depending on the choice of the detuning. We investigate how this detuning effects the position information of the atom inside the standing wave field in upper-level and lower-level coupling schemes of Autler- Townes microscopy. We show an enhancement in precision position measurement by factor of at least 4 in upper-level coupling scheme due to the quantum interference phenomenon. This enhancement is not observed in lower-level coupling scheme where the quantum interference is not taking place. \n \nWe also consider a system where a three-level atom is interacting with a monochromatic radiation field in such a way that the decay takes place from upper level to the intermediate level with a rate T and from intermediate level to lower level at a rate γ. This type of system exhibits a non stationary scattered light signal. We report the results of the spontaneous emission spectrum for non stationary scattered light signal by using the definition of time-dependent physical spectrum. This is a rare example of problems where time-dependent physical spectrum can be calculated exactly. We study the characteristics of the spontaneous spectrum for a resonant and off-resonant case and show that this physical spectrum recovers the results of earlier work quite successfully. We also show that the decay rate r disturbs the atomic coherence and finally eliminates the dark line from the center of the spontaneous spectrum. Here we only consider upper-level coupling case for the time-dependent spontaneous spectrum because in lower-level coupling case the system automatically evolved a pumping mechanism due to the coupling of ground level to the upper level via radiation field. Thus a steady-state limit exists in lower-level coupling scheme. \n \nWe investigate the phenomenon of atom localization by using the non stationary Autler-Townes microscopy. The decay rate T reduces the precision in position measurement which is consistent with the results of the non stationary spontaneous emission spectrum. This is due to the fact that for the upper-level coupling case, the standing wave field is coupled to atomic transition and it induces a coherence in the upper-level atomic transition but the spontaneous decay from the upper level to the intermediate level disturbs this coherence. When the effect of the spontaneous decay dominates the coherence effect the quantum interference phenomenon vanishes and thus the precision in localization reduces.
We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.