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Journal of Physics B Atomic Molecular and Optical Physics

The micromaser as a quantum clock

Christian Bracher

Published Jun 14, 1997• 24 citations
Publisher

Abstract

The interaction of light and matter provides a `clock' which allows us to extract characteristic timescales of quantum motion. Two-level atoms temporarily subjected to a radiation field will undergo Rabi oscillations, and the rotation angle of the corresponding Bloch vector serves as a measure of the interaction time. The approach is closely related to proposed `Larmor clock' experiments exploiting particle spin precession in a magnetic field, and gives some insight into how the usual notion of time emerges from quantum mechanics in its classical limit. The usage of the micromaser device for an experimental determination of quantum reflection, transmission, and dwell times is discussed.

DOI
10.1088/0953-4075/30/11/021

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The interaction of light and matter provides a clock' which allows us to extract characteristic timescales of quantum motion. Two-level atoms temporarily subjected to a radiation field will undergo Rabi oscillations, and the rotation angle of the corresponding Bloch vector serves as a measure of the interaction time. The approach is closely related to proposed Larmor clock' experiments exploiting particle spin precession in a magnetic field, and gives some insight into how the usual notion of time emerges from quantum mechanics in its classical limit. The usage of the micromaser device for an experimental determination of quantum reflection, transmission, and dwell times is discussed.
Baz' and Rybachenko have proposed the use of the Larmor precession as a clock to measure the time it takes a particle to traverse a barrier. An applied magnetic field is confined to the barrier. The spin of the incident particles is polarized perpendicular to this field. The extent of the Larmor precession occurring during transmission is used as a measurement of the time spent traversing the barrier. However, the particles tunneling through an opaque barrier also acquire a spin component parallel to the field since particles with spin parallel to the field have a higher transmission probability than particles with spin antiparallel to the field. Similar effects are actually used to polarize electrons and neutrons. An interpretation of this experiment compares the results with an approach which determines the traversal time by studying transmission of particles through a time-modulated barrier. This leads to three characteristic times describing the interaction of particles with a barrier. A dwell time measures the average time interval during which a particle interacts with the barrier whether it is reflected or transmitted at the end of its stay, a traversal time measures the time interval during which a particle interacts with the barrier if it is finally transmitted, and a reflection time measures the interaction time of a reflected particle.
A spin precessing in a magnetic field is often used as a quantum clock, for example in tunneling-time measurements. We show that such a clock can exist in a coherent superposition of opposite temporal orientations, treating the arrow of time as a quantum two-level system. A Mach-Zehnder interferometer with equal and opposite magnetic fields provides a simple implementation, enabling interference between forward and backward evolution and Bell-type tests of temporal coherence. Extending the framework to relativistic dynamics reveals that the Dirac Hamiltonian describes an intrinsic coupling between a spin qubit and a time qubit, with matter and antimatter corresponding to opposite poles on the temporal Bloch sphere.
There are only fistful of systems in physics that can be described by an exact theory from first principles and, at the same time, can be investigated under experimental conditions approaching the idealized theoretical ones. The one-atom-maser or micromaser provides such an example, making a detailed study of the fundamental properties of the atom-field interaction possible. The situation realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a cavity field. In the micromaser the atoms have a dual purpose of both pumping the field and also probing it via measurements of the outgoing atoms. Any other means of measuring the field inside the resonator has the detrimental effect of lowering its Q-factor and thereby the photon storage time. The long photon storage time of the resonator allows for the decay of the field to be negligible during the passage of an atom and its interaction with the field. The behavior of atoms in a cavity is governed by the oscillatory exchange of energy between the atoms and the field, which is called Rabi oscillation. For cavity fields in the vacuum and few photon number states (Fock states), Rabi oscillations have been measured in the past. To prevent thermal effects from polluting the pure number states these experiments were performed at low temperatures (below 1 K). However, the observed resolution of the Rabi oscillations measurements was quite disappointing (only about 2% of the predicted theoretical value) and precluded more ambitious experiments like atom-atom correlations or time resolved investigations of the maser field dynamics. The observed contrast of Rabi oscillations can be considered as a figure of merit for the experimental resolution of quantum features of a maser field. Therefore, a high resolution in the measurements of Rabi oscillations is crucial. This thesis describes the methods and improvements applied to enhance the resolution of Rabi oscillations by a factor of 8. The following upgrades and developments proved to be crucial in this work: 1) The base temperature of the cryogenic system was lowered to 0.3 K, i.e. one third of the original value. At the same time, the time during which the system remains at the base temperature was improved by almost of an order of magnitude (to more than 12 h). 2) For the promotion of the atoms to the Rydberg regime new three-step diode laser setup was constructed. The excitation efficiency compared to the old dye laser was increased by two orders. Using top-of-fringe stabilization with new spectroscopic methods, specially designed error detection and feedback schemes as well as state-of-the-art PID regulators the continuous locking of lasers is about 8 h (compared to about 20 min with the old dye laser system). 3) The flexibility of using the three step excitation allows to excite different maser states and for the first time to investigate pure maser transition. 4) Various improvements on the atomic oven and the channeltron detection unit led to the reliable and stable production and detection of the atomic beam. Observed distribution of the atomic beam statistics reaches to within 6% the Poisson limit which is expected in the absence of experimental imperfections. 5) New developed techniques in magnetic field compensation allow to perform such measurements with two orders of magnitude better accuracy compared to the previous experiments. To demonstrate the new capabilities of the apparatus and to apply its improved resolution of quantum fields we performed a previously impossible in-depth analysis of mean photon number and the atomic inversion produced by a micromaser for various detunings between the cavity- and atomic resonance frequency.
We exploit analogies between tunneling electrons and evanescent electromagnetic waves to construct and operate an optical Larmor clock. In the electronic Larmor clock, the tunneling time is proportional to the amount of precession the electronic spin undergoes while interacting with a weak, barrier-confined magnetic field. In the optical scheme, the analogy to the spin is made via Stokes parameters, and an optical retarder is shown to be analogous to the magnetic field. A magnetized tunnel barrier consists of a thin film of uniaxial liquid crystal between two high-index prisms. To operate the clock, we measure the Stokes parameters of the polarized laser beam transmitted through the barrier. By varying the wavelength of the incident light, we use the clock to study tunneling through barriers of various thicknesses. \textcopyright{} 1996 The American Physical Society.
We consider the neutron-optical phenomena that emerge during the coherent interaction of a neutron with a sample when the neutron spin precesses in a magnetic field. As follows from general considerations, such an interaction gives rise to an extra precession phase, which is added to the Larmor precession phase. This phenomenon can be interpreted as a manifestation of the time delay due to a finite time of the neutron-sample interaction. The Larmor neutron spin precession with a constant frequency serves as a clock for measuring this time delay. We used such a clock to directly measure the difference between the neutron velocity in matter and its vacuum value. We also present the results of the first experiments in which Larmor clocks were used to measure the neutron tunneling time in the resonance of a quasi-bound state and the Bragg diffraction time. Prospects for further applications of the method are discussed.
A controversy surrounding the "tunnelling time problem" stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space. For this reason, the problem is often approached from an "operational" angle. Typically, one tries to mimic, in a quantum case, an experiment which yields the desired result for a classical particle. One such approach is based on the use of a Larmor clock. We show that the difficulty with applying a non-perturbing Larmor clock in order to "time" a classically forbidden transition arises from the quantum Uncertainty Principle. We also demonstrate that for this reason a Larmor time (in fact, any Larmor time) cannot be interpreted as a physical time interval. We provide a theoretical description of the quantities measured by the clock.