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Physical Review A

Preparation of a pure number state and measurement of the photon statistics in a high-Qmicromaser

Joachim Krause, Marlan O. Scully, Thomas Walther, HERBERT WALTHER

Published Feb 1, 1989• 99 citations
Publisher

Abstract

Two schemes to prepare pure number states in a high-Q micromaser with Rydberg atoms are proposed. In the first experiment the atoms are probed after the interaction with the cavity field and the number state is obtained via state reduction. In the second experiment the interaction time of ionic Rydberg atoms with the maser field can be controlled via an electric accelerating field. The velocity of the ions is adjusted in such a way that every ion emits a photon and the total number of photons is exactly known via the total number of passing ions. It is also shown how the photon statistics in the micromaser in general can be probed via the outgoing atoms.

DOI
10.1103/physreva.39.1915

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State reduction and |n〉 -state preparation in a high- Q micromaser

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Experiments with the One-atom-maser

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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.

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P. Domokos, M. Brune, J. M. Raimond +2 more

A single two-level atom can be used to prepare an arbitrary photon number state (Fock state) in a high Q cavity . The atom undergoes a controlled succession of interactions with two cavity modes. One of them contains a coherent field. The atom transfers photons one by one from this field to the initially empty second mode. The scheme can be extended to prepare a quantum superposition of the vacuum with a Fock state, a highly non-classical situation. We discuss the feasibility of the experiment with our present Rydberg-atom cavity QED set-up.

The European Physical Journal D•Jan 1, 1998•55 citations
Two schemes to prepare pure number states in a high-Q micromaser with Rydberg atoms are proposed. In the first experiment the atoms are probed after the interaction with the cavity field and the number state is obtained via state reduction. In the second experiment the interaction time of ionic Rydberg atoms with the maser field can be controlled via an electric accelerating field. The velocity of the ions is adjusted in such a way that every ion emits a photon and the total number of photons is exactly known via the total number of passing ions. It is also shown how the photon statistics in the micromaser in general can be probed via the outgoing atoms.
The long lifetime of photons in a high-QQQ micromaser cavity is used to generate a ∣n〉|n〉∣n〉-state maser field by injecting atoms, one at a time. Every atom is probed for its excitation after leaving the cavity so that the precise number of photons in the field is known. We calculate the probability of obtaining nnn photons after mmm atoms have passed the cavity.
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.
Experiments with the one-atom maser1 have demonstrated that it is possible to study the interaction of a single atom with a single-mode of a resonant electromagnetic field in a cavity. The atoms used in these experiments are Rydberg atoms with a very large principal quantum number. Another important ingredient is the superconducting cavity: The quality factor is high enough for a periodic energy exchange between atom and cavity field to be observed; i.e., the relaxation time of the cavity field is larger than the characteristic time of the atom-field interaction, which is given by the reciprocal of the Rabi frequency. It is therefore possible to perform experiments on the dynamics of the atom-field interaction. Some of the features are explicitly a consequence of the quantum nature of the electromagnetic field.2 With a new cavity (quality factor 3 × 1010) it could be demonstrated that the statistics of the photons in the cavity is sub-Poissonian; in suitable conditions it is even possible to generate number states. Using number states of the single-atom maser novel quantum interference experiments can be performed giving new insight in the wave particle duality.
We describe the first investigation of the nonclassical radiation field of a micromaser. The maser cavity is cooled to 0.5 K to exclude thermal photons and has a quality factor 3\ifmmode\times\else\texttimes\fi{}1010{10}^{10}1010. Velocity-selected Rydberg atoms pump the maser. The photon statistics in the cavity are measured via the statistics of the atoms leaving the cavity in the lower maser level. Taking into account a detection efficiency of 10%, their fluctuations are reduced up to 40% below the Poisson level. This corresponds to photon-number fluctuations in the cavity of up to 70% below the vacuum-state limit.
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.
A single two-level atom can be used to prepare an arbitrary photon number state (Fock state) in a high Q cavity . The atom undergoes a controlled succession of interactions with two cavity modes. One of them contains a coherent field. The atom transfers photons one by one from this field to the initially empty second mode. The scheme can be extended to prepare a quantum superposition of the vacuum with a Fock state, a highly non-classical situation. We discuss the feasibility of the experiment with our present Rydberg-atom cavity QED set-up.