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Journal of Time and Frequency

Study of Ramsey Interferometry with Three-level Tonks-Girardeau Gas

Shougang Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The Ramsey's method of separated oscillatory fields is applied to study Ramsey interferometry but using a Tonks-Girardeau model that describes a coherent one-dimensional gas of ultracold bosons with strong interactions.Under the equal detuning,the interference fringes width can be narrowed by increasing the Rabi frequency and the field-crossing time.Moreover,we gain further insight into the quantum projection noise.In contrast to a two-level TG gas,our results illustrate that the modulation of the total number of three-level atoms and the external fields tend to lower the quantum noise limit,so as to reduce the interference of the noise to the strongly interacting bosonic Tonks-Girardeau gas.The investigation on the atomic interferometry is a great theoretical guidance to the research of quantum frequency standard.

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The Ramsey's method of separated oscillatory fields is applied to study Ramsey interferometry but using a Tonks-Girardeau model that describes a coherent one-dimensional gas of ultracold bosons with strong interactions.Under the equal detuning,the interference fringes width can be narrowed by increasing the Rabi frequency and the field-crossing time.Moreover,we gain further insight into the quantum projection noise.In contrast to a two-level TG gas,our results illustrate that the modulation of the total number of three-level atoms and the external fields tend to lower the quantum noise limit,so as to reduce the interference of the noise to the strongly interacting bosonic Tonks-Girardeau gas.The investigation on the atomic interferometry is a great theoretical guidance to the research of quantum frequency standard.
We propose a solvable generalization of the Tonks-Girardeau model that describes a coherent one-dimensional (1D) gas of cold two-level bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by idealized, infinitely strong contact potentials, with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal bosons. The dual system of this gas, an ideal gas of two-level fermions coupled by the interaction with the separated fields, produces the same fringes and noise fluctuations. The cases of time-separated and spatially separated fields are studied. For spatially separated fields the fringes may be broadened slightly by increasing the number of particles, but only for large particle numbers far from present experiments with Tonks-Girardeau gases. The uncertainty in the determination of the atomic transition frequency diminishes, essentially with the inverse root of the particle number. The difficulties to implement the model experimentally and possible shortcomings of strongly interacting 1D gases for frequency standards and atomic clocks are discussed.
First we discuss briefly the importance of time and time keeping, explaining the basic functioning of clocks in general and of atomic clocks based on Ramsey interferometry in particular. The usefulness of cold atoms is discussed, as well as their limits if Bose-Einstein condensates are used. We study as an alternative a different cold-atom regime: the Tonks-Girardeau (TG) gas of tightly confined and strongly interacting bosons. The TG gas is reviewed and then generalized for two-level atoms. Finally, we explore the combination of Ramsey interferometry and TG gases.
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.
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 report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.
Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.