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Journal of Optics B Quantum and Semiclassical Optics

Generation of Fock states in the micromaser

Benjamin T. H. Varcoe, S. Brattke, HERBERT WALTHER

Published Apr 1, 2000• 24 citations
Publisher

Abstract

The recent observation of trapping states in the micromaser not only gave strong indications that the cavity field was quantized but also that the field was held in a number state or Fock state for long periods of time. We extend this measurement to show that under achievable experimental conditions, steady-state Fock generation is possible. Additionally, we show how the cavity field can be projected onto a number state using state reduction and then probed to determine the field state.

DOI
10.1088/1464-4266/2/2/316

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The recent observation of trapping states in the micromaser not only gave strong indications that the cavity field was quantized but also that the field was held in a number state or Fock state for long periods of time. We extend this measurement to show that under achievable experimental conditions, steady-state Fock generation is possible. Additionally, we show how the cavity field can be projected onto a number state using state reduction and then probed to determine the field state.
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.
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.
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.
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.
Coherent superpositions of quantum states are very sensitive to coupling to the environment. The fluctuations associated with this coupling tend to wash out quantum phases, so that in practice only quantum mixtures are observed at the macroscopic level. This problem has been the object of recent interest in connection with measurement theory (Schrodinger cat). Theoretical predictions indicate that the decay of quantum coherences in the so-called pointer basis is amplified by a factor proportional to a measure of the distance in Hilbert space between the states. Micromasers offer a possible experimental tool to investigate the decay of such coherences. Theoretical studies of a lossless version of the micromaster have shown the existence of trapping states | n q 〉 of the cavity mode. These number states are such that atoms injected in the upper state into the cavity experience a 2qπ interaction with the field. Cavity states of the form | ψ 〉 = Σ q C q | n q 〉 are easily shown to be dynamic steady states of the system. Number states are not a pointer basis for the micromaser, and our theoretical results will evidence the qualitative difference in the nature of coherence decay between this and previously studied cases. Because the decay times of micromaser cavities are typically of the order of hundreds of milliseconds, our results should be amenable to experimental verification.