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

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

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

Published Aug 20, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.828171

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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.
Large ensembles of uncorrelated atoms are extensively used as precise sensors of time, rotation, and gravity, and for tests of fundamental physics. The quantum nature of the sensors imposes a limit on their ultimate precision. Larger ensembles of N atoms can be used to average the quantum noise as 1/√N, a scaling known as the standard quantum limit. However, the ensemble size may be limited by technical constraints and/or atom-atom collisions -- a fundamental distinction from photon-based sensors. Learning to prepare entangled states of large ensembles with noise properties below the standard quantum limit will be key to extending both the precision and/or bandwidth of atomic sensors. More broadly, the generation and application of entanglement to solve problems is a core goal of quantum information science being pursued in both atomic and solid state systems.\nIn this thesis, we utilize the tools of cavity-QED to prepare entangled spin-squeezed states with 3.4(6) dB improvement in spectroscopic sensitivity over the standard quantum limit. The collective atomic spin is composed of the two-level clock states of 87Rb confined in a medium finesse F = 710 optical cavity. We employ cavity-aided quantum non-demolition measurements of the vacuum Rabi splitting to measure and subtract out the quantum projection noise of the collective spin state, preparing states with collective atomic spin projection noise 4.9(6) dB below the projection noise level. The conditionally reduced spin noise combined with the measured 1.5(3) dB reduction in the mean spin length implies a net 3.4(6) dB spectroscopic enhancement or conditional squeezing as defined by the Wineland criterion. Our method does not require single particle addressability and is applied to a spectroscopically large ensemble of N = 7 x 105 atoms using two collective population measurements, with the whole squeezing operation taking ~ 150 μs. The gain in sensitivity is spectroscopically equivalent to the enhancement obtained had we created > 105 pairs of maximally entangled qubits, demonstrating the power of a top-down approach for entangling large ensembles. The nondemolition probing of atomic populations via the vacuum Rabi splitting is also of broad interest for non-destructively reading out a wide variety of both atomic and solid state qubits.
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.
Optical atomic clocks with unrivaled precision and accuracy have advanced the frontier of precision measurement science and opened new avenues for exploring fundamental physics. A fundamental limitation on clock precision is the standard quantum limit (SQL), which stems from the uncorrelated projection noise of each atom. State-of-the-art optical lattice clocks interrogate large ensembles to minimize the SQL, but density-dependent frequency shifts pose challenges to scaling the atom number. The SQL can be surpassed, however, by leveraging entanglement, though it remains an open problem to achieve quantum advantage from spin squeezing at state-of-the-art stability levels. Here, we demonstrate clock performance beyond the SQL, achieving a fractional frequency precision of 1.1×10^{-18} for a single spin-squeezed clock. With cavity-based quantum nondemolition measurements, we prepare two spin-squeezed ensembles of ∼30 000 strontium atoms confined in a two-dimensional optical lattice. A synchronous clock comparison with an interrogation time of 61 ms achieves a metrological improvement of 2.0(2) dB beyond the SQL, after correcting for state preparation and measurement errors. These results establish the most precise entanglement-enhanced clock to date and offer a powerful platform for exploring the interplay of gravity and quantum entanglement.
Ultimate quantum fluctuations which limit the fundamental precision in metrology can be only reduced by entanglement of particles. In particular, squeezing of the fluctuations called the spin projection noise by means of generation of entanglement in an ensemble of atoms can improve the precision of spectroscopy and of atomic clocks. A powerful tool for generation of multiparticle entanglement is a quantum nondemolition measurement (QND). We will describe the fundamentals of QND measurement of atomic collective state with light and present a recent experiment [1] where this method has been used to reduce the projection noise on the clock transition in an ensemble of 105 cold and trapped Cesium atoms. Another method for generation of spin squeezing via electron-nucleus entanglement applicable only for atoms with angular momentum higher than ½ will be also discussed [2].
We demonstrate spin squeezing and entanglement in a large-spin system via quantum non-demolition measurement. We make non-destructive, projection-noise-limited collective spin measurements on an ensemble of up to in 8.4 × 105 laser-cooled 87Rb atoms in the f = 1 hyperfine ground state. A dynamically-decoupled probing scheme [Phys. Rev. Lett. 105, 093602 (2010)] prevents probe-induced decoherence. Repeated measurements show correlations beyond the standard quantum limit, indicating generation of a spin-squeezed state with up to −3.6 dB of noise reduction and −2.6 dB of metrologically-relevant squeezing.