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Physical Review A

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

Joachim Krause, Marlan O. Scully, HERBERT WALTHER

Published Nov 1, 1987• 183 citations
Publisher

Abstract

The long lifetime of photons in a high-$Q$ micromaser cavity is used to generate a $|n〉$-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 $n$ photons after $m$ atoms have passed the cavity.

DOI
10.1103/physreva.36.4547

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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.
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.
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.
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.
We suggest an iterative, maximum-likelihood–based, method to reconstruct the photon number distribution of the steady-state cavity field of a micromaser starting from the statistics of the atoms leaving the cavity after the interaction. The scheme is based on measuring the atomic populations of probe atoms for different interaction times and works effectively using a small number of atoms and a limited sampling of the interaction times. The method has been tested by numerically simulated experiments showing that it may be reliably used in any micromaser regime, leading to high-fidelity reconstructions for single-peaked distributions as well as for double-peaked ones and for trapping states.
Quality factor of up to 4/spl times/10/sup 10/, corresponding to an average lifetime of a photon in the cavity of 0.3 s, are achieved. The photon lifetime is thus much longer than the interaction time of an atom with the maser field. The atoms used are rubidium Rydberg atoms pumped by laser excitation into the upper maser level, 63P/sub 3/2/, the lower maser level is either the 61D/sub 5/2/ or the 61D/sub 3/2/ depending on the cavity frequency. The atom field dynamics is observed by measuring the atoms in the upper or lower maser levels after the cavity. During the interaction the field in the cavity consists only of single or a few photons, nevertheless, it is possible to study the interaction in detail.
For an arbitrary initial photon probability distribution in a micromaser cavity, it is shown that photon-number eigenstates can be induced by passing excited atoms, one at a time, through the cavity. The photon number can be predicted for a given velocity of excited atoms. It is found that the total photon energy inside a lossless cavity becomes saturated once a photon number state is achieved. It is also possible to find more than one number states, each occurs with a certain probability under particular initial conditions. If the injected atoms have a small velocity distribution Av around v, then only a near-number state with the predicted photon number is possible. For Av/v - 0.1, the photon probability in the cavity can still maintain subpoisson distribution until sufficiently large number of excited atoms have passed. Other novel phenomena are also found in two-photon processes.