Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Overcoming the quantum projection noise (QPN) limit without preparation of the spin-squeezed state

Nobuyasu Shiga, Makoto Takeuchi

Published Sep 8, 2011• 0 citations
Publisher

Abstract

Atomic clocks have reached the Quantum Projection Noise (QPN) limit of stability and it has been proposed to use the entangled atomic ensemble in order to overcome the QPN limit. We have proposed a new method to lock the phase of the Local Oscillator (LO) to the atomic phase and call, "atomic phase lock (APL)." This APL could possibly overcome the QPN limit without need of preparing the entangled atomic ensemble. Traditional Ramsey method destroys the coherence of the atomic spin due to the projection measurement at each cycle. This destruction and initialization of the phase at each cycle introduce additional noise and the performance of the atomic clock is limited at the white frequency noise level. APL employs dispersion measurements, i.e. Faraday rotation, in order to measure the phase difference without destroying the atomic phase. By repeating the measurement cycle with sufficiently small dead time, one can suppress the LO noise down to white phase noise level, achieving the τ-1 dependence of the Allan variance that can eventually overcome the QPN limit in long term. We are preparing a proof-of-principle experiment using the ensemble of trapped 171Yb+ ions with hyperfine splitting (12.6 GHz) as a clock transition and report the current status of the experiment as well.

DOI
10.1117/12.892674

Related papers

Locking the local oscillator phase to the atomic phase via weak measurement

Nobuyasu Shiga, Makoto Takeuchi

We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.

•Jan 1, 2012•32 citations

Locking the local oscillator phase to the atomic phase via weak measurement

N Shiga, M Takeuchi

A new method is proposed to reduce the frequency noise of a local oscillator to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This method, which we call 'atomic phase lock (APL)', uses weak measurement to monitor the phase in the Ramsey method and repeat the cycle without initialization of the phase. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirmed that with APL, the Allan deviation is averaged down at a maximum rate that is proportional to the inverse of the total measurement time, τ −1 . In contrast, current atomic clocks that use projection measurement suppress the noise only to the white frequency noise level, in which case the Allan deviation scales as τ −1/2 . Faraday rotation is one way to achieve weak measurement for APL. The strength of Faraday rotation with 171 Yb + ions trapped in a linear rf-trap is evaluated, and the performance of APL is discussed. The main source of decoherence is a spontaneous emission, induced by the probe beam for Faraday rotation measurement. The Faraday rotation measurement can be repeated until the decoherence becomes comparable to the signal-to-noise ratio of the measurement. The number of cycles for a realistic experimental parameter is estimated to be ∼100.

arXiv:1107.5176•New Journal of Physics•Feb 15, 2012•34 citations

Accelerating the averaging rate of atomic ensemble clock stability using atomic phase lock

Nobuyasu Shiga, Michiaki Mizuno, Kohta Kido +2 more

We experimentally demonstrated that the stability of an atomic clock improves at its fastest rate τ −1 (where τ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (an atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over three measurement cycles, and thereby improved the stability scaling from to τ −1 during the three measurement cycles. This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise.

arXiv:1401.1288•New Journal of Physics•Jul 22, 2014•8 citations

Direct comparison of two spin squeezed optical clocks below the quantum projection noise limit

John Martin Robinson, Maya Miklos, Yee Ming Tso +5 more

Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x10$^4$ atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10$^{-17}$, without subtracting any technical noise contributions.

arXiv:2211.08621•Nov 16, 2022•5 citations

Preparation of reduced-quantum-uncertainty input states for an atomic clock

Monika Schleier-Smith, Ian D. Leroux, Vladan Vuletić

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 20, 2009•2 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.

arXiv:2104.14309•Physical Review A•May 19, 2022•8 citations
Atomic clocks have reached the Quantum Projection Noise (QPN) limit of stability and it has been proposed to use the entangled atomic ensemble in order to overcome the QPN limit. We have proposed a new method to lock the phase of the Local Oscillator (LO) to the atomic phase and call, "atomic phase lock (APL)." This APL could possibly overcome the QPN limit without need of preparing the entangled atomic ensemble. Traditional Ramsey method destroys the coherence of the atomic spin due to the projection measurement at each cycle. This destruction and initialization of the phase at each cycle introduce additional noise and the performance of the atomic clock is limited at the white frequency noise level. APL employs dispersion measurements, i.e. Faraday rotation, in order to measure the phase difference without destroying the atomic phase. By repeating the measurement cycle with sufficiently small dead time, one can suppress the LO noise down to white phase noise level, achieving the τ-1 dependence of the Allan variance that can eventually overcome the QPN limit in long term. We are preparing a proof-of-principle experiment using the ensemble of trapped 171Yb+ ions with hyperfine splitting (12.6 GHz) as a clock transition and report the current status of the experiment as well.
We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.
A new method is proposed to reduce the frequency noise of a local oscillator to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This method, which we call 'atomic phase lock (APL)', uses weak measurement to monitor the phase in the Ramsey method and repeat the cycle without initialization of the phase. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirmed that with APL, the Allan deviation is averaged down at a maximum rate that is proportional to the inverse of the total measurement time, τ −1 . In contrast, current atomic clocks that use projection measurement suppress the noise only to the white frequency noise level, in which case the Allan deviation scales as τ −1/2 . Faraday rotation is one way to achieve weak measurement for APL. The strength of Faraday rotation with 171 Yb + ions trapped in a linear rf-trap is evaluated, and the performance of APL is discussed. The main source of decoherence is a spontaneous emission, induced by the probe beam for Faraday rotation measurement. The Faraday rotation measurement can be repeated until the decoherence becomes comparable to the signal-to-noise ratio of the measurement. The number of cycles for a realistic experimental parameter is estimated to be ∼100.
We experimentally demonstrated that the stability of an atomic clock improves at its fastest rate τ −1 (where τ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (an atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over three measurement cycles, and thereby improved the stability scaling from to τ −1 during the three measurement cycles. This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise.
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x104^44 atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10−17^{-17}−17, without subtracting any technical noise contributions.
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.
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.