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Results in Physics

The quantum measurement effect of interaction without interaction for an atomic beam

Yong-Yi Huang

Published Dec 28, 2016• 0 citations
Publisher

Abstract

When an atomic beam collectively and harmonically vibrates perpendicular to the wave vector of the beam, the number of atoms reaching the atomic detector will have a vibrant factor Δt/T if the measurement time interval Δt is shorter than the period T. This new quantum mechanical measurement effect for an atomic beam is called interaction without interaction: though the translational motion of the atomic beam does not interact with its collective and transverse harmonic vibration, the latter will have an effect on the measured number of atoms associated with the former. From the new measurement effect the classical harmonic vibration’s period is evaluated. We give a clear physical picture and a satisfactory physical interpretation for the measurement effect based on the Copenhagen interpretation of quantum mechanics. We present an experimental proposal to verify this measurement effect for an ion beam instead of an atomic beam.

DOI
10.1016/j.rinp.2016.12.040

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When an atomic beam collectively and harmonically vibrates perpendicular to the wave vector of the beam, the number of atoms reaching the atomic detector will have a vibrant factor Δt/T if the measurement time interval Δt is shorter than the period T. This new quantum mechanical measurement effect for an atomic beam is called interaction without interaction: though the translational motion of the atomic beam does not interact with its collective and transverse harmonic vibration, the latter will have an effect on the measured number of atoms associated with the former. From the new measurement effect the classical harmonic vibration’s period is evaluated. We give a clear physical picture and a satisfactory physical interpretation for the measurement effect based on the Copenhagen interpretation of quantum mechanics. We present an experimental proposal to verify this measurement effect for an ion beam instead of an atomic beam.
We propose a simplest detector of harmonic vibrations with micro amplitudes and low frequencies, i.e. a detector consisting of one atomic beam. Here, the atomic beam is induced by a plane harmonic wave and has classical collective harmonic vibrations, whose vibrant directions are perpendicular to the wave vectors of the atomic beam. Compared with a detector consisting of an atomic Mach-Zehnder interferometer, the new detector has two advantages: (1) it is suitable for the detection of harmonic vibrations induced either by a longitudinal plane harmonic wave or by using a transverse plane harmonic wave: (2) the quantum noise fluctuation of the atomic beam is exactly zero. We present the principle for detecting classical harmonic vibrations with micro amplitudes and low frequencies by using the new detector. The frequency of a classical harmonic vibration with a micro amplitude can be evaluated by measuring the variations in the mean numbers of atoms arriving at the atomic detector.
The so-called 'interaction-free' measurement is a very interesting quantum effect that allows discovering the presence of an opaque object in a given spatial domain, with the probability that the object absorbs a photon being, in principle, as low as desired. This probability is bounded from below only by a value of the order of 1/ωτ, where ω is the frequency of light and τ is the measurement time. This corresponds to the average absorbed energy of the order of /τ. The 'interaction-free' technique can also be used to measure the coordinate of an object but only under the condition that the object is prepared in a special 'discretized' quantum state. Such is, for instance, the state of a ponderomotive meter of electromagnetic energy, which, in principle, enables the interaction-free' measurement of the energy contained in an electromagnetic cavity. Estimations show that with modern experimental equipment and with the help of 'interaction-free' measurement, single atoms can be registered inside optical cavities.
Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729 nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).
This paper aims at studying the time-dependent effects involved in the photoassociation reaction for a sample of cold alkali-metal atoms, within a two-channel model where the vibrational motion in the excited state is coupled by laser light to the continuum state describing two colliding atoms in the lowest triplet electronic state $(a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}).$ Both photodissociation and photoassociation processes are considered at a time scale shorter than the radiative lifetime, so that spontaneous emission does not have to be considered. The characteristic times are then the vibrational period in the excited state, which for alkali-metal dimers can be estimated of the order of a few hundreds of picoseconds, and the Rabi period, depending upon the laser intensity. Numerical calculations using wave-packet propagation are performed for the coupling of the vibrational motion in the Cs21g(6s+6p3/2){\mathrm{Cs}}_{2}{1}_{g}{(6s+6p}_{3/2})Cs2​1g​(6s+6p3/2​) and ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}(6s+6s)$ channels by a cw laser slightly red detuned relative to the D2{\mathrm{D}}_{2}D2​ resonance line. The results show Rabi oscillations in the populations of the two channels during time intervals when the vibrational motion is stopped at the outer turning point. At intensities of $\ensuremath{\approx}250\mathrm{kW}{\mathrm{cm}}^{\ensuremath{-}2},$ a new characteristic time appears, a factor of 2 larger than the classical vibrational period, which corresponds to vibrational motion in the upper adiabatic potential created by the coupling. Such an effect modifies the scattering length for collisions in the lower state, and it clearly opens a possibility of control by tuning the laser intensity.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.