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Fortschritte der Physik

Fock State Rabi Oscillations; A Building Block for the Observation of New Phenomena in Quantum Optics

Benjamin T. H. Varcoe, S. Brattke, Berthold‐Georg Englert, HERBERT WALTHER

Published May 1, 2000• 8 citations
Publisher

Abstract

In recent experiments it was demonstrated that number or Fock states of the one-atom maser can be generated. Two types of experiments have been performed. In the first one the Fock states are achieved in steady state via the so-called trapping states of the micromaser field. In the second experiment the number states were generated in a dynamical experiment by state reduction. In the latter case the generated field was afterwards probed by observing the dynamics of a probe atom in the field. The fact that Fock states of the micromaser field can be realised leads to new applications of the micromaser one of them is the generation of a many particle entanglement of the GHZ type.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<679::aid-prop679>3.0.co;2-l

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Generation of Fock states in the micromaser

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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.

•Jan 1, 2009•0 citations

Trapping States in the Micromaser

M. Weidinger, Benjamin T. H. Varcoe, R. Heerlein +1 more

Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.

Physical Review Letters•May 10, 1999•251 citations
In recent experiments it was demonstrated that number or Fock states of the one-atom maser can be generated. Two types of experiments have been performed. In the first one the Fock states are achieved in steady state via the so-called trapping states of the micromaser field. In the second experiment the number states were generated in a dynamical experiment by state reduction. In the latter case the generated field was afterwards probed by observing the dynamics of a probe atom in the field. The fact that Fock states of the micromaser field can be realised leads to new applications of the micromaser one of them is the generation of a many particle entanglement of the GHZ type.
Summary form only given. We report on the first generation of Fock states using the micromaser. In order to produce the field, a flux of excited state atoms is passed through the cavity. The Fock states are realized in two ways: firstly in the steady state by using the trapping condition of the maser field, and secondly using state reduction of the pumping atoms. In the second experiment the purity of the Fock state could be investigated in detail by sending an additional probe atom into the cavity and investigating the dynamics of the photon exchange.
The one atom maser is an archetype experiment of quantum optics, where the interaction is between the basic quantum components of a single atoms and a single mode field, uncluttered by unwanted side effects. Thus the one atom maser is able to examine the most fundamental aspects of the atom light interaction. In this paper we review three of the most recent experiments on the very topical subject of photon Fock state creation. Namely the creation Fock states via trapping states, dynamical Fock state preparation using state reduction of lower state atoms and finally the creation of Fock states on demand. In the two decades since its first operation, the one atom maser continues to operate at the forefront of quantum optics research having produced many first class results. We present some taste of future, as we turn the micromaser to quantum computing and the creation of exotic entangled states.
Many applications in quantum information or quantum computing require radiation with a fixed number of photons (called Fock or number states) and this special issue demonstrates the real increase in interest in this area. In this paper, we review three recent papers in which we discussed the creation of photon number states in the micromaser and discuss new results. In the first experiment, Fock states were created in steady state via trapping states. Some new results are presented in this section showing a remarkable improvement of our ability to create these states. We then review a second method of dynamic Fock state creation using state reduction of lower state atoms. In this experiment, we also observed the purity of the Fock state that was created via the observation of Rabi oscillations of a probe atom. Finally, we discuss the results of the third experiment that we performed which was an experimental demonstration of a method of creating Fock states on demand.
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.
Trapping states in the one-atom maser or micromaser are predicted by maser theory and are a direct consequence of the quantization of the electromagnetic field. They have been found in our experiment when the inversion of atoms leaving the cavity is observed while the interaction time is scanned. They correspond to quantum states of the atom-cavity system and under certain conditions represent Fock states. The trapping states occur when the atom-field dynamics complete a full evolution (or multiples thereof). Owing to feedback through the maser dynamics, a stabilization of the photon number in the steady state field of the maser cavity is achieved.