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arXiv:2009.05006 · Physical Review A

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

Enlong Wang, Gunjan Verma, Jonathan N. Tinsley, N. Poli, Leonardo Salvi

Published Feb 16, 2021• 6 citations
arXivHTMLPDF

Abstract

We demonstrate a method of light phase shift measurement using a high-finesse optical ring cavity which exhibits reduced phase noise due to cavity length fluctuations. Two laser beams with a frequency difference of one cavity free spectral range are simultaneously resonant with the cavity, demonstrating noise correlations in the error signals due to the common-mode cavity length fluctuations. The differential error signal shows a 30 dB reduction in cavity noise down to the noise floor in a frequency range up to half the cavity linewidth ($\ensuremath{\delta}\ensuremath{\nu}/2\ensuremath{\simeq}30$ kHz). Various noise sources are analyzed and their contributions to the noise floor are evaluated. Additionally, we apply this noise-reduced phase shift measurement scheme in a simulated spin-squeezing experiment where we have achieved a factor of 40 improvement in phase sensitivity with a phase resolution of 0.7 mrad, which may remove one important barrier against attaining highly spin-squeezed states. The demonstrated method provides a flexible situation by using an optical ring cavity and two independent beams. This method can find direct application to nondestructive measurements in quantum systems, such as for the generation of spin-squeezed states in atom interferometers and atomic clocks.

DOI
10.1103/physreva.103.022609

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We demonstrate a method of light phase shift measurement using a high-finesse optical ring cavity which exhibits reduced phase noise due to cavity length fluctuations. Two laser beams with a frequency difference of one cavity free spectral range are simultaneously resonant with the cavity, demonstrating noise correlations in the error signals due to the common-mode cavity length fluctuations. The differential error signal shows a 30 dB reduction in cavity noise down to the noise floor in a frequency range up to half the cavity linewidth (\ensuremathδ\ensuremathν/2\ensuremath≃30\ensuremath{\delta}\ensuremath{\nu}/2\ensuremath{\simeq}30\ensuremathδ\ensuremathν/2\ensuremath≃30 kHz). Various noise sources are analyzed and their contributions to the noise floor are evaluated. Additionally, we apply this noise-reduced phase shift measurement scheme in a simulated spin-squeezing experiment where we have achieved a factor of 40 improvement in phase sensitivity with a phase resolution of 0.7 mrad, which may remove one important barrier against attaining highly spin-squeezed states. The demonstrated method provides a flexible situation by using an optical ring cavity and two independent beams. This method can find direct application to nondestructive measurements in quantum systems, such as for the generation of spin-squeezed states in atom interferometers and atomic clocks.
Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states, accounting for common-mode phase noise spanning the full 2π2π2π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit. Specifically, we identify optimal squeezed states that minimize the differential phase variance, scaling as N−2/3N^{-2/3}N−2/3, while eliminating bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér-Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
This thesis investigates the generation of atomic spin-squeezed states by quantum non-demolition (QND) measurements in a high-finesse optical cavity. Cold atom interferometry has demonstrated state of the art performance for the measurement of tiny rotations, accelerations and time. The sensitivity of atom interferometers has already reached the atomic shot noise level, a limit that could be overcome by the use of non-classical atomic states. In this context, we developed a crossed high-finesse cavity resonating both at 1560 nm and 780 nm. Laser light at 1560 nm injected in the cavity generates a far off resonance optical dipole trap where Rb 87 cold atoms are loaded from a magneto-optical trap. The lifetime of the atoms in this dipole trap is limited by the residual background collisions, indicating that further evaporation process should be effective. The concepts of QND measurement are introduced and a wavefunction formalism that describes the spin-squeezing dynamics of the atomic state is discussed. This formalism is applied to practical measurement apparatus that are the Mach-Zehnder interferometer and the heterodyne detection. Experimentally, this non-destructive measurement was implemented at 780 nm in a frequency modulation scheme strongly immune to noise. The influence of this non-demolition probe on the atomic sample has been characterized in single pass and this tool has been applied to follow in real time the state of atomic interferometers. In addition to this work, a narrow linewidth Raman laser suitable for high precision spectroscopy was implemented with cold atoms as the gain medium.
Atomic clocks have reached the Standard Quantum Limit (SQL) of precision,1 set by the projection noise inherent in measurements on uncorrelated atoms. It is possible to overcome this limit by entangling the atoms to generate a "squeezed state" of the atomic ensemble. We use the collective interaction of an atomic ensemble with a far-detuned light field in an optical resonator to prepare squeezed states by two different methods: quantum non-demolition (QND) measurement and Hamiltonian evolution. We apply both methods to an ensemble of 5 x 104 87Rb atoms in a superposition of hyperfine clock states. We measure the suppression of projection noise and compare it to the accompanying reduction in signal, thereby quantifying the net gain in spectroscopic sensitivity. By QND measurement, with resolution up to 9 dB below the projection noise level, we achieve 3.0(8) dB of metrologically relevant squeezing. Whereas the measurement-based approach relies on knowledge of the (randomly distributed) measurement outcome to produce a conditionally squeezed state, the method of Hamiltonian evolution produces a known squeezed state independent of detector performance. We mimic the dynamics of the one-axis twisting Hamiltonian, proposed as a generator of squeezed states by Kitagawa and Ueda,2 by using the atom-induced frequency shift of the resonator mode and the corresponding resonator-field-induced shift of the atomic transition frequency to introduce an effective interaction among the atoms. The resulting deterministic squeezing is sufficient to allow a 6.0(4) dB improvement in spectroscopic sensitivity over the SQL.
Abstract Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states of N atoms, accounting for common-mode phase noise spanning the full 2 π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit (SQL). Specifically, we identify optimal squeezed states that minimize the differential phase uncertainty, scaling as N − 2 / 3 , thus overcoming the SQL by a factor N 1 / 6 , while eliminating the bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér–Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
Lasers with high spectral purity are indispensable for optical clocks and coherent manipulation of atomic and molecular qubits for applications such as quantum computing and quantum simulation. Stabilisation of the laser to a reference can provide a narrow linewidth and high spectral purity. However, widely-used diode lasers exhibit fast phase noise that prevents high fidelity qubit manipulation. Here we demonstrate a self-injection locked diode laser system utilizing a medium finesse cavity. The cavity not only provides a stable resonance frequency, but at the same time acts as a low-pass filter for phase noise beyond the cavity linewidth of around 100 kHz, resulting in low phase noise from dc to the injection lock limit. We model the expected laser performance and benchmark it using a single trapped 40^{40}40Ca+^{+}+-ion as a spectrum analyser. We show that the fast phase noise of the laser at relevant Fourier frequencies of 100 kHz to >2 MHz is suppressed to a noise floor of between -110 dBc/Hz and -120 dBc/Hz, an improvement of 20 to 30 dB over state-of-the-art Pound-Drever-Hall-stabilized extended-cavity diode lasers. This strong suppression avoids incoherent (spurious) spin flips during manipulation of optical qubits and improves laser-driven gates in using diode lasers with applications in quantum logic spectroscopy, quantum simulation and quantum computation.