Laser noise imposed limitations of ensemble quantum metrology

Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential-light-shift-free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling with τ being the interrogation time. We employ a technique using decoherence-free subspaces first introduced in Dorner (2012 New J. Phys. 14 043011 ) which can restore the scaling with the square root of the inverse particle number . Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differential-light-shift-free magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling with τ being the interrogation time. We employ a technique using decoherence-free subspaces first introduced in Dorner (2012 New J. Phys. 14 043011 ) which can restore the scaling with the square root of the inverse particle number . Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.

arXiv:1605.00874Journal of Physics B Atomic Molecular and Optical PhysicsNov 22, 201611 citations

Protected subspace Ramsey spectroscopy

Laurin Ostermann, David Plankensteiner, Helmut Ritsch +1 more

We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit super-radiant collective decay and dipole-dipole induced frequency shifts, recent results [L. Ostermann, H. Ritsch, and C. Genes, Phys. Rev. Lett. 111, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an in-depth analysis of this ``protected subspace Ramsey technique'' using improved analytical modeling and numerical simulations including larger three-dimensional (3D) samples. Surprisingly we find that using subradiant states of $N$ particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than $1/\sqrt{N}$ . Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit super-radiant collective decay and dipole-dipole induced frequency shifts, recent results [L. Ostermann, H. Ritsch, and C. Genes, Phys. Rev. Lett. 111, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an in-depth analysis of this ``protected subspace Ramsey technique'' using improved analytical modeling and numerical simulations including larger three-dimensional (3D) samples. Surprisingly we find that using subradiant states of $N$ particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than $1/\sqrt{N}$. Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.

arXiv:1407.8420Physical Review ANov 11, 201417 citations

Leveraging correlated laser noise to improve optical frequency comparisons

Ethan Clements, M. Bohman, May E. Kim +14 more

Laser noise usually limits the stability of optical frequency ratio measurements, limiting the speed and precision one can compare two atomic frequency standards. In this talk I will describe two methods, correlation and differential spectroscopy, which utilize correlations in laser noise to increase the achievable interrogation time and thus increase the frequency comparison stability. Correlation spectroscopy is a technique which uses a parity measurement following a synchronized Ramsey interrogation to measure the relative frequency of two similar frequency atomic clocks. With this technique we achieve a measurement instability of (4×10^(-16))⁄√(τ⁄s) for a comparison of two single 27Al+ ion clocks. Differential spectroscopy uses an atomic clock with low projection noise, here a 171Yb lattice clock, to correct the phase noise of a second, higher frequency clock’s local oscillator thereby reducing the measurement instability to the level of the first. This can be further extended using two lattice clocks in a zero dead time configuration to correct the phase noise beyond the interrogation time reachable for a single Yb lattice clock. With these techniques we achieve measurement stabilities of (2.5×10^(-16))⁄√(τ⁄s) and (2×10^(-16))⁄√(τ⁄s) for a comparison between a single 27Al+ ion clock and a 171Yb lattice clock running as single clock and in a zero dead time configuration respectively. In addition to these techniques, I will also discuss recent progress towards characterizing the systematics of the NIST 40Ca+/27Al+ optical atomic clock.Laser noise usually limits the stability of optical frequency ratio measurements, limiting the speed and precision one can compare two atomic frequency standards. In this talk I will describe two methods, correlation and differential spectroscopy, which utilize correlations in laser noise to increase the achievable interrogation time and thus increase the frequency comparison stability. Correlation spectroscopy is a technique which uses a parity measurement following a synchronized Ramsey interrogation to measure the relative frequency of two similar frequency atomic clocks. With this technique we achieve a measurement instability of (4×10^(-16))⁄√(τ⁄s) for a comparison of two single 27Al+ ion clocks. Differential spectroscopy uses an atomic clock with low projection noise, here a 171Yb lattice clock, to correct the phase noise of a second, higher frequency clock’s local oscillator thereby reducing the measurement instability to the level of the first. This can be further extended using two lattice clocks in a zero dead time configuration to correct the phase noise beyond the interrogation time reachable for a single Yb lattice clock. With these techniques we achieve measurement stabilities of (2.5×10^(-16))⁄√(τ⁄s) and (2×10^(-16))⁄√(τ⁄s) for a comparison between a single 27Al+ ion clock and a 171Yb lattice clock running as single clock and in a zero dead time configuration respectively. In addition to these techniques, I will also discuss recent progress towards characterizing the systematics of the NIST 40Ca+/27Al+ optical atomic clock.

Optical and Quantum Sensing and Precision Metrology IIMar 9, 20220 citations

Spin squeezing can only improve clocks with small atom number

Marius Schulte, Christian Lisdat, Piet O. Schmidt +2 more

We show that the stability of an optical atomic clock can only be improved by spin squeezed states for ensembles below a critical particle number. This limitation results from a trade-off between measurement noise and instabilities due to limited laser coherence. Our results apply to the case of cyclic Ramsey interrogations on a single atomic ensemble with dead time between each measurement. The combination of analytical models for projection noise, dead time noise (Dick effect) and laser phase noise allows quantitative predictions of the critical particle number and the optimal clock stability for a given dead time and laser noise. Our analytical predictions are confirmed by numerical simulations of the closed servo loop of an optical atomic clock.We show that the stability of an optical atomic clock can only be improved by spin squeezed states for ensembles below a critical particle number. This limitation results from a trade-off between measurement noise and instabilities due to limited laser coherence. Our results apply to the case of cyclic Ramsey interrogations on a single atomic ensemble with dead time between each measurement. The combination of analytical models for projection noise, dead time noise (Dick effect) and laser phase noise allows quantitative predictions of the critical particle number and the optimal clock stability for a given dead time and laser noise. Our analytical predictions are confirmed by numerical simulations of the closed servo loop of an optical atomic clock.

Nov 3, 20190 citations

Improved absolute clock stability by the joint interrogation of two atomic ensembles

Weidong Li, Shuyuan Wu, Augusto Smerzi +1 more

Improving the clock stability is of fundamental importance for the development of quantum-enhanced metrology. One of the main limitations arises from the randomly fluctuating local oscillator (LO) frequency, which introduces ``phase slips'' for long interrogation times and hence the failure of the frequency-feedback loop. Here we propose a strategy to improve the stability of atomic clocks by interrogating two atomic ensembles sharing the same LO. The two ensembles are prepared in coherent spin states pointing along orthogonal directions in the Bloch sphere. While standard Ramsey interrogation can only determine phases unambiguously in the interval $[\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2]$, the joint interrogation allows for an extension to $[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}]$, resulting in a relaxed restriction of the Ramsey time and improvement of absolute clock stability. Theoretical predictions are supported by ab initio numerical simulation for white and correlated LO noise. While our basic protocol uses uncorrelated atoms, we further extended it to include spin-squeezing and further improving the scaling of clock stability with the number of atoms. Our protocol can be readily tested in current state-of-the-art experiments.Improving the clock stability is of fundamental importance for the development of quantum-enhanced metrology. One of the main limitations arises from the randomly fluctuating local oscillator (LO) frequency, which introduces ``phase slips'' for long interrogation times and hence the failure of the frequency-feedback loop. Here we propose a strategy to improve the stability of atomic clocks by interrogating two atomic ensembles sharing the same LO. The two ensembles are prepared in coherent spin states pointing along orthogonal directions in the Bloch sphere. While standard Ramsey interrogation can only determine phases unambiguously in the interval $[\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2]$, the joint interrogation allows for an extension to $[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}]$, resulting in a relaxed restriction of the Ramsey time and improvement of absolute clock stability. Theoretical predictions are supported by ab initio numerical simulation for white and correlated LO noise. While our basic protocol uses uncorrelated atoms, we further extended it to include spin-squeezing and further improving the scaling of clock stability with the number of atoms. Our protocol can be readily tested in current state-of-the-art experiments.

arXiv:2104.14309Physical Review AMay 19, 20228 citations

Bayesian frequency metrology with optimal Ramsey interferometry in optical atomic clocks

Timm Kielinski, Klemens Hammerer

Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as one of the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to optical atomic clocks primarily limited by laser noise. To incorporate frequency fluctuations directly into the theoretical model, we consider a Bayesian framework. In this context, we review fundamental bounds arising in Bayesian estimation theory, which serve as a benchmark throughout this work. We investigate the trade-off between entanglement-enhanced sensitivity and robustness against laser noise in order to identify optimal initial states, measurement schemes and estimation strategies. Beside standard protocols based on coherent spin states, spin-squeezed states and Greenberger-Horne-Zeilinger states, we consider variational Ramsey protocols implemented via low-depth quantum circuits based on one-axis twisting operations to approach optimal stability. In particular, we review known and identify new optimal Ramsey interrogation schemes for a variety of scenarios, including different experimental platforms, ensemble sizes and regimes characterized by a wide range of interrogation durations and dead times. Hence, this work establishes a comprehensive theoretical framework for optimizing Ramsey interrogation schemes, providing guidance for the development of next-generation optical atomic clocks.Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as one of the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to optical atomic clocks primarily limited by laser noise. To incorporate frequency fluctuations directly into the theoretical model, we consider a Bayesian framework. In this context, we review fundamental bounds arising in Bayesian estimation theory, which serve as a benchmark throughout this work. We investigate the trade-off between entanglement-enhanced sensitivity and robustness against laser noise in order to identify optimal initial states, measurement schemes and estimation strategies. Beside standard protocols based on coherent spin states, spin-squeezed states and Greenberger-Horne-Zeilinger states, we consider variational Ramsey protocols implemented via low-depth quantum circuits based on one-axis twisting operations to approach optimal stability. In particular, we review known and identify new optimal Ramsey interrogation schemes for a variety of scenarios, including different experimental platforms, ensemble sizes and regimes characterized by a wide range of interrogation durations and dead times. Hence, this work establishes a comprehensive theoretical framework for optimizing Ramsey interrogation schemes, providing guidance for the development of next-generation optical atomic clocks.

arXiv:2505.04287Reports on Progress in PhysicsNov 19, 20251 citation

N

particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than

1/\sqrt{N}

. Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.