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Optics Letters

Ramsey interferometry of a bosonic Josephson junction in an optical cavity

Sheng-Chang Li, Fu-Quan Dou, Libin Fu

Published Sep 25, 2017• 4 citations
Publisher

Abstract

We investigate the nonlinear Ramsey interferometry of a bosonic Josephson junction coupled to an optical cavity by applying two identical pumping field pulses separated by a holding field in the time domain. When the holding field is absent, we show that the atomic Ramsey fringes are sensitive to both the cavity-pump detuning and the initial state, and their periods can encode the information on both the atom-field coupling and the atom-atom interaction. For a weak holding field, we find that the fringes characterized by the oscillation of the intra-cavity photon number can completely reflect the frequency information of the atomic interference due to the weak atom-cavity coupling. This finding allows a nondestructive observation of the atomic Ramsey fringes via the cavity transmission spectra.

DOI
10.1364/ol.42.003952

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We investigate the nonlinear Ramsey interferometry of a bosonic Josephson junction coupled to an optical cavity by applying two identical pumping field pulses separated by a holding field in the time domain. When the holding field is absent, we show that the atomic Ramsey fringes are sensitive to both the cavity-pump detuning and the initial state, and their periods can encode the information on both the atom-field coupling and the atom-atom interaction. For a weak holding field, we find that the fringes characterized by the oscillation of the intra-cavity photon number can completely reflect the frequency information of the atomic interference due to the weak atom-cavity coupling. This finding allows a nondestructive observation of the atomic Ramsey fringes via the cavity transmission spectra.
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.
We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in the time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.
Taking Rosen-Zener tunneling as the underlying process，a scheme to achieve nonlinear Ramsey interferometry with a two-component trapped Bose-Einstein condensate is proposed. Abundant nonlinear Ramsey interference fringes are observed in time domain by the numerical simulations and these fringes are very different from the sinusoidal pattern for linear Ramsey interference due to the dominant nonlinear interaction between atoms. Furthermore，Fourier transformation results show that the fundamental frequency of Ramsey fringes can exactly reflect the information of nonlinearity or asymmetry. This finding provides an opportunity to measure atomic properties via measuring the frequency of fringes.
A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.
We demonstrate an experimental observation of coherent population trapping-Ramsey interference in cold 87 Rb atoms by employing the time-domain separated oscillatory fields' method. The interference fringe with line width of 80Hz is obtained. We propose a novel method to measure the cold atom number. The measurement is insensitive to the pump beam intensity, the single photon detuning and even the initial state population. We use this method to normalize the interference signal and to improve the signal-to-noise ratio significantly.
We propose a scheme of obtaining Ramsey fringes based on pulsed coherent optical information storage. Unlike the usual frequency references where the Ramsey fringes are obtained by detecting the population of a certain state, we get the Ramsey fringes by detecting the atomic coherence. The central line of the Ramsey fringes can be used as a frequency reference in an absorption-cell-based atomic frequency standard. This scheme is free of light shifts as the interrogating process is separated from the optical pumping process, and the cavity pulling effect is negligible due to the low QQQ requirement. Encoding the Ramsey interference into the retrieval light pulse has the merit of high signal-to-noise ratio. This scheme is promising for building small, compact, and stable atomic clocks.