Squeezing on Momentum States for Atom Interferometry

Abstract

We propose and analyse a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition of strontium atoms in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based atom interferometer with large diffraction orders. The applicability of this technique can be extended also to small diffraction orders and large atom numbers by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling ∆φ ∼ N −3/4 , where N is the atom number. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the Standard Quantum Limit.A major effort in the field of atom interferometry [1] is focused on increasing the instrument sensitivity, either by enhancing the momentum transferred by the light onto the atoms [2,3] or by increasing the interrogation time [3][4][5][6]. By applying differential schemes, many systematics and noise sources can be efficiently rejected as common-mode effects [7,8], and one eventually meets the fundamental atom shot noise limit that arises from the uncorrelated phase noise of different atoms. The minimum phase resolution allowed by uncorrelated atomic states is the Standard Quantum Limit (SQL) ∆φ SQL = 1/ √ N , where N is the atom number. This limit can be overcome by introducing correlations between the individual particles, thereby producing squeezed atomic states, potentially reaching the Heisenberg limit ∆φ H = 1/N [9, 10]. Many schemes have been studied both theoretically [11,12] and experimentally [13][14][15][16][17][18][19][20][21] with about 20 dB noise reduction compared to the SQL [22,23]. The key feature of most of these schemes is the enhanced atom-light interaction in an optical resonator. Many experiments with optical resonators involve trapping the atoms in an optical potential generated by the resonator itself and inducing atomic correlations through internal atomic states. Because of these features, optical resonators are well suited for atomic clocks beyond the SQL. The implementation of these methods in atom interferometry remains, however, a challenging task.In this Letter we propose and analyse a scheme that generates squeezed momentum states [9,24] for atom interferometry. In particular, we consider the production of squeezed states of the atomic center-of-mass motion by dispersive probing of a momentum-state superposition of ultracold strontium (Sr) atoms in an optical ring resonator. On the one hand, for the bosonic isotopes of strontium, the choice of the atomic species is motivated by its expected immunity to stray fields in atom interferometers and by the possibility of attaining long coherence times in quantum interference [25,26]. On the other hand, the presence of narrow intercombination transiti...

Testing gravity with cold atom interferometry: results and prospects

“…For a given momentum transfer and interrogation time, the interferometer sensitivity is limited by the so-called quantum projection noise. Work is in progress to overcome this limit and potentially reach the Heisenberg limit by introducing quantum correlations between the individual atoms thus producing squeezed atomic states [102][103][104][105][106].…”

Driving quantum correlated atom-pairs from a Bose–Einstein condensate

“…A squeezed state refers to a quantum state that has a reduced uncertainty in one degree of freedom ('squeezed') at the expense of increased uncertainty in a canonically conjugate variable [24][25][26][27][28][29][30]. Such states have been extensively studied in quantum optics and atomic physics due to their utility in quantum metrology for producing measurement precision that exceeds the limits derived from classical states.…”

Method for the differential measurement of phase shifts induced by atoms in an optical ring cavity

“…The proposed scheme has several advantages over the general noise cancellation scheme in a Fabry-Pérot cavity with single phase-modulated light [8,[26][27][28][29]. First, the ring cavity geometry allows for the manipulation [30] and probing [31] of atomic momentum states as well as of internal states. Second, the scheme where two independent beams are simultaneously resonant with the cavity is very flexible in practical applications, enabling independent phase modulation of the two beams.…”

“…The proposed system demonstrates close to 30 dB reduction in the cavity length fluctuations down to the noise floor in a frequency range up to half the cavity linewidth (δν/2 30 kHz). We further apply this measurement scheme in a simulated spin-squeezing experiment [31] where a cavity phase shift measurement is performed with a 200 μs averaging time. We demonstrate an improvement in phase sensitivity by a factor of 40 with a phase resolution of 0.7 mrad.…”