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1. Imaging-based cavity optomechanics

   https://doi.org/10.1117/12.2676081  

   Pluchar, Christian M; Agrawal, Aman R; Wilson, Dalziel J (October 2023, SPIE)

   Dholakia, Kishan; Spalding, Gabriel C (Ed.)

   Cavity optomechanics has led to advances in quantum sensing, optical manipulation of mechanical systems, and macroscopic quantum physics. However, previous studies have typically focused on cavity optomechanical coupling to translational degrees of freedom, such as the drum mode of a membrane, which modifies the amplitude and phase of the light field. Here, we discuss recent advances in “imaging-based” cavity optomechanics – where information about the mechanical resonator’s motion is imprinted onto the spatial mode of the optical field. Torsion modes are naturally measured with this coupling and are interesting for applications such as precision torque sensing, tests of gravity, and measurements of angular displacement at and beyond the standard quantum limit. In our experiment, the high-Q torsion mode of a Si3N4 nanoribbon modulates the spatial mode of an optical cavity with degenerate transverse modes. We demonstrate an enhancement of angular sensitivity read out with a split photodetector, and differentiate the “spatial” optomechanical coupling found in our system from traditional dispersive coupling. We discuss the potential for imaging-based quantum optomechanics experiments, including pondermotive squeezing and quantum back-action evasion in an angular displacement measurement. 

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2. Bosonic pair production and squeezing for optical phase measurements in long-lived dipoles coupled to a cavity

   https://doi.org/10.48550/arXiv.2204.13090  

   Sundar, B.; Barberena, D.; Piñeiro Orioli, A.; Chu, A.; Thompson, J.K.; Rey, A.M.; Lewis-Swan, R.J. (October 2022, ArXivorg)

   We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing (TMS) of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for the observation of continuous variable entanglement in atomic systems and associated applications in next-generation optical atomic clocks. 

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3. Entanglement-enhanced matter-wave interferometry in a high-finesse cavity

   https://doi.org/10.1038/s41586-022-05197-9  

   Greve, Graham P.; Luo, Chengyi; Wu, Baochen; Thompson, James K. (October 2022, Nature)

   Abstract An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit 1–3  set by projections of individual atoms. Large amounts of entanglement 4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles 4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity $$3\,.\,{4}_{-0.9}^{+1.1}$$ 3 . 4 − 0.9 + 1.1  dB and $$2\,.\,{5}_{-0.6}^{+0.6}$$ 2 . 5 − 0.6 + 0.6  dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity $$1\,.\,{7}_{-0.5}^{+0.5}$$ 1 . 7 − 0.5 + 0.5  dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors 17,18 , searches for new physics, particles and fields 19–23 , future advanced gravitational wave detectors 24,25 and accessing beyond mean-field quantum many-body physics 26–30 . 

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4. Cavity piezo-mechanics for superconducting-nanophotonic quantum interface

   https://doi.org/10.1038/s41467-020-17053-3  

   Han, Xu; Fu, Wei; Zhong, Changchun; Zou, Chang-Ling; Xu, Yuntao; Sayem, Ayed Al; Xu, Mingrui; Wang, Sihao; Cheng, Risheng; Jiang, Liang; et al (June 2020, Nature Communications)

   Abstract Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10 GHz phonons are resonantly coupled with photons in a superconducting cavity and a nanophotonic cavity at the same time. Taking advantage of the large piezo-mechanical cooperativity (C_em ~7) and the enhanced optomechanical coupling boosted by a pulsed optical pump, we demonstrate coherent interactions at cryogenic temperatures via the observation of efficient microwave-optical photon conversion. This hybrid interface makes a substantial step towards quantum communication at large scale, as well as novel explorations in microwave-optical photon entanglement and quantum sensing mediated by gigahertz phonons. 

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5. Page curves and typical entanglement in linear optics

   https://doi.org/10.22331/q-2023-05-23-1017  

   Iosue, Joseph T.; Ehrenberg, Adam; Hangleiter, Dominik; Deshpande, Abhinav; Gorshkov, Alexey V. (May 2023, Quantum)

   Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity. 

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