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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Effect of detuning on generation of the photon-number state in m-photon micromaser via the atomic measurement

Ziaohu Zhang, Xiping Zheng, Xiaoping Yang

Published Jul 1, 1990• 0 citations

Abstract

The Photonnusber eigenstate (PNE state) generated in a oneatos sphoton sicrolaser systes via the atosic seasuresent for the outofresonance case is shown. The effect of detuning on the probability of obtaining state after having k atoss passed the cavity is discussed. THEORY A beau of lowdensity twolevel atoss is injected into ahighQ cavity at such a low rate that at lost one atos at a t lie is present inside the cay i ty. The cavi ty loss is negi igible. Consider a twolevel atos interacting with a singlesode field via the iphoton transition for the near ly resonant case. The effect i ye Has i lton ian for th is systes in the RWA is Hf cact + q/2)+i1 A q/2+t1g( a'' cy. . Q" ( 1) where L(. )i() is the detuning and ''fi is the energy difference between the two levels of atos g is the iphoton transition atosfield coupling constant Q and *'' are the annihilation and creation operators of the field and ca is the frequency of field a3 and a. are the Pauli spin operators. Assuse that the field is in PNE state at a tue t1 in which the ith excited atol is just going to be injected. r is the tile for the ith atoi to pass through the cavity. The density operator p (t+t ) is p (t+t )U( i: ) p

DOI: 10.1117/12.22245

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The Photonnusber eigenstate (PNE state) generated in a oneatos sphoton sicrolaser systes via the atosic seasuresent for the outofresonance case is shown. The effect of detuning on the probability of obtaining state after having k atoss passed the cavity is discussed. THEORY A beau of lowdensity twolevel atoss is injected into ahighQ cavity at such a low rate that at lost one atos at a t lie is present inside the cay i ty. The cavi ty loss is negi igible. Consider a twolevel atos interacting with a singlesode field via the iphoton transition for the near ly resonant case. The effect i ye Has i lton ian for th is systes in the RWA is Hf cact + q/2)+i1 A q/2+t1g( a'' cy. . Q" ( 1) where L(. )i() is the detuning and ''fi is the energy difference between the two levels of atos g is the iphoton transition atosfield coupling constant Q and *'' are the annihilation and creation operators of the field and ca is the frequency of field a3 and a. are the Pauli spin operators. Assuse that the field is in PNE state at a tue t1 in which the ith excited atol is just going to be injected. r is the tile for the ith atoi to pass through the cavity. The density operator p (t+t ) is p (t+t )U( i: ) p

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.

The quantum theory of the cold atom micromaser including the effects of gravity is established in the general case where the cavity mode and the atomic transition frequencies are detuned. We show that atoms which classically would not reach the interaction region are able to emit a photon inside the cavity. The system turns out to be extremely sensitive to the detuning and in particular to its sign. A method to solve the equations of motion for non resonant atom-field interaction and arbitrary cavity modes is presented.

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.

A short review of the theoretical studies of the cold atom micromaser (mazer) is presented. Existing models are then improved by considering more general working conditions. Especially, the mazer physics is investigated in the situation where a detuning between the cavity mode and the atomic transition frequency is present. Interesting new effects are pointed out. Especially, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. The transmission probability of ultracold atoms through a micromaser is also studied and we generalize previous results established in the resonant case. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a nonresonant field inside the cavity. This manuscript is a summary of Martin's master thesis and articles [Phys. Rev. A 67, 053804 (2003)] and [Eur. Phys. J. D 29, 133 (2004)].

We investigate the quantum dynamics of a two-photon micromaser pumped by atoms injected in the superposition state of the upper and intermediate levels. We simulate a master equation governing the system by the Monte Carlo wavefunction approach and analyse the steady-state behaviour as a function of the atomic transit time. The atomic coherence can effectively enhance the intensity and sub-Poissonian of the cavity field as compared with the atomic mixture. It is also discovered that the phase of the cavity field can be shifted by adjusting the detuning between the atom and field. This result shows that it is possible to manipulate the phase of the cavity field by detuning, due to atomic coherence.