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Optical and Quantum Sensing and Precision Metrology II

Near-unitary spin squeezing with ytterbium (Conference Presentation)

Boris Braverman, Akio Kawasaki, Edwin Pedrozo-Peñafiel, Simone Colombo, Chi Shu, Zeyang Li, Enrique Mendez, Megan Yamoah, Leonardo Salvi, Daisuke Akamatsu, Yanhong Xiao, Vladan Vuletić

Published Mar 9, 2020• 0 citations
Publisher

Abstract

State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).

DOI
10.1117/12.2552065

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Bulletin of the American Physical Society•Jun 12, 2015•4 citations
State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).
Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in ^{171}Yb, an optical lattice clock atom. The collective nuclear spin of ∼10^{3} atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical-clock transition of ^{171}Yb.
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.
Measurements with quantum limited resolution have important applications in metrology and sensing, including atomic clocks, atom interferometry, and magnetometry. We perform a quantum-non-demolition measurement on a collective angular momentum of a million spin-4 Cs atoms with high optical depth in our work. Quantum mechanics limits the measurement's resolution to what is known as the standard quantum limit (SQL) when there is no entanglement between the individual atoms. We can generate entanglement between atoms to create spin squeezed states through quantum backaction, improving the measurement sensitivity by 5.5 dB relative to the SQL. We have recently rebuilt the entire experiment inside a state-of-the-art magnetic shield of mu-metal and aluminum. This upgrade has drastically mitigated classical control errors in the spin squeezing experiment. Furthermore, the ensemble's sensitivity to magnetic fields allows us to make precise measurements of the magnetic field environment. Using closed-loop feedback, we use our atomic magnetometer to measure magnetic fields 4.3 dB below the SQL. The shielded environment will allow us to optimize the magnetometer and sets the stage for future experiments to use the closed-loop control to explore more complicated quantum dynamics.
Spin squeezing is a form of entanglement that can improve the stability of quantum sensors operating with multiple particles, by inducing inter-particle correlations that redistribute the quantum projection noise. Previous analyses of potential metrological gain when using spin squeezing were performed on theoretically ideal states, without incorporating experimental imperfections or inherent limitations which result in non-unitary quantum state evolution. Here, we show that potential gains in clock stability are substantially reduced when the spin squeezing is non-unitary, and derive analytic formulas for the clock performance as a function of squeezing, excess spin noise, and interferometer contrast. Our results highlight the importance of creating and employing nearly pure entangled states for improving atomic clocks.
Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.