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Ramsey Interferometry with Quantized Fields

G. S. Agarwal, Pradyumna K. Pathak, Marlan O. Scully

Published Jul 19, 2002• 0 citations
OpenAlex

Abstract

Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this case we show how two atom (like two photon) interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of first atom. PACS number(s): 03.75.Dg, 03.65.Ud, 42.50.-p Typeset using REVTEX 1 The method of using spatially separated fields as proposed by Ramsey has been proved to be very useful for high resolution work. It was originally proposed as a technique in the microwave domain [1] which was then extended to studies in optical domain [2]. More recently this technique has been used very successfully in the studies of quantum entanglement resulting from the interaction of atoms with radiation in a high quality cavity. In this context Ramsey technique enables one to study the entanglement in different basis of states

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Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this case we show how two atom (like two photon) interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of first atom. PACS number(s): 03.75.Dg, 03.65.Ud, 42.50.-p Typeset using REVTEX 1 The method of using spatially separated fields as proposed by Ramsey has been proved to be very useful for high resolution work. It was originally proposed as a technique in the microwave domain [1] which was then extended to studies in optical domain [2]. More recently this technique has been used very successfully in the studies of quantum entanglement resulting from the interaction of atoms with radiation in a high quality cavity. In this context Ramsey technique enables one to study the entanglement in different basis of states
Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have a precise number of photons. However, in this case we show how an analog of Hanbury-Brown Twiss photon-photon correlation interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of the first atom. Interferences are restored by working with fields at a single-photon level. Generation of entangled states including states such as $|2,0〉{+e}^{i\ensuremath{\theta}}|0,2〉$ is discussed.
The interference fringes of an atomic Ramsey interferometer may be narrowed if the two separated fields have different frequencies and their phase difference is controlled. For spatially separated fields, their width depends inversely on the free flight time of ground state atoms before entering the first field region in addition to the time between the fields. The narrowing effect is stable with respect to velocity fluctuations and for realistic mode functions. We also show that systematic phase shifts and phase fluctuations do not aggravate the frequency offset of the standard (one-frequency) Ramsey method.
In Ramsey atomic interferometry, a superposition of atomic states is produced by a mechanism completely equivalent (for experimental purposes) to interaction with a classical field. Since this property holds, in the case of Rydberg atoms, for temperatures close to absolute zero and field intensities of the order of a single photon, the question arises as to why the quantum nature of the field can be neglected. We model the passage of an atom through a Ramsey zone and show that, in order to explain the phenomenon, correlation properties between three subsystems and strong cavity dissipation turn out to be the essential physical ingredients leading to classical behavior.
We investigate Ramsey interferometry for two separated fields oscillating with different frequencies. It is shown that the interplay between average and relative detuning leads to interference effects not present in the standard, single-frequency setup. For a large free-flight time of ground-state atoms before entering the first field region, the Ramsey fringes with respect to the relative detuning become much narrower than the usual ones. The stability of these effects with respect to phase or velocity fluctuations is discussed.
We describe the optimum detection procedure to follow in order to measure by atomic interferometry the number of photons present in a cavity by using a Quantum nondemolition scheme. The method we discuss is the one recently introduced by Brune et al. [1, 2], in which the field intensity is detected by recording atomic interferences in a Ramsey type set up. A succession of two-level atoms interacts with the cavity field which is the analog of a birefringent retarding plate for the atomic wave function. The information is acquired in the form of binary digits (atoms detected in one level or the other). We discuss an optimal strategy which yields the value of the photon number with a number of atoms of the order of the base 2 logarithm of the field photon number dispersion. The procedure described here is the one we intend to use in an experiment in preparation.