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Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.

We demonstrate an inertia sensitive atom interferometer optically guided inside a 22-cm-long negative curvature hollow-core photonic crystal fiber with an interferometer time of 20 ms. The result prolongs the previous fiber guided atom interferometer time by three orders of magnitude. The improvement arises from the realization of in-fiber {\Lambda}-enhanced gray molasses and delta-kick cooling to cool atoms from 32 {\mu}K to below 1 {\mu}K in 4 ms. The in-fiber cooling overcomes the inevitable heating during the atom loading process and allows a shallow guiding optical potential to minimize decoherence. Our results permit bringing atoms close to source fields for sensing and could lead to compact inertial quantum sensors with a sub-millimeter resolution.

Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.

Quantum engineering using photonic structures offer new capabilities for atom-photon interactions for quantum optics and atomic physics, which could eventually lead to integrated quantum devices. Despite the rapid progress in the variety of structures, coherent excitation of the motional states of atoms in a photonic waveguide using guided modes has yet to be demonstrated. Here, we use the waveguide mode of a hollow-core photonic crystal fibre to manipulate the mechanical Fock states of single atoms in a harmonic potential inside the fibre. We create a large array of Schr\"odinger cat states, a quintessential feature of quantum physics and a key element in quantum information processing and metrology, of approximately 15000 atoms along the fibre by entangling the electronic state with the coherent harmonic oscillator state of each individual atom. Our results provide a useful step for quantum information and simulation with a wide range of photonic waveguide systems.

Light storage in an optical fiber is an attractive component in quantum optical delay line technologies. Although silica-core optical fibers are excellent in transmitting broadband optical signals, it is challenging to tailor their dispersive property to slow down a light pulse or store it in the silica-core for a long delay time. Coupling a dispersive and coherent medium with an optical fiber is promising in supporting long optical delay. Here, we load cold Rb atomic vapor into an optical trap inside a hollow-core photonic crystal fiber, and store the phase of the light in a long-lived spin-wave formed by atoms and retrieve it after a fully controllable delay time using electromagnetically-induced-transparency (EIT). We achieve over 50 ms of storage time and the result is equivalent to 8.7x10^-5 dB s^-1 of propagation loss in an optical fiber. Our demonstration could be used for buffering and regulating classical and quantum information flow between remote networks.

Traditionally, measuring the center-of-mass (c.m.) velocity of an atomic ensemble relies on measuring the Doppler shift of the absorption spectrum of single atoms in the ensemble. Mapping out the velocity distribution of the ensemble is indispensable when determining the c.m. velocity using this technique. As a result, highly sensitive measurements require preparation of an ensemble with a narrow Doppler width. Here, we use a dispersive measurement of light passing through a moving room temperature atomic vapor cell to determine the velocity of the cell in a single shot with a short-term sensitivity of 5.5 $\mu$m s$^{-1}$ Hz$^{-1/2}$. The dispersion of the medium is enhanced by creating quantum interference through an auxiliary transition for the probe light under electromagnetically induced transparency condition. In contrast to measurement of single atoms, this method is based on the collective motion of atoms and can sense the c.m. velocity of an ensemble without knowing its velocity distribution. Our results improve the previous measurements by 3 orders of magnitude and can be used to design a compact motional sensor based on thermal atoms.

Confining particles in hollow-core photonic crystal fibers has opened up new prospects to scale up the distance and time over which particles can be made to interact with light. However, maintaining long-lived quantum spin coherence and/or transporting it over macroscopic distances in a waveguide remain challenging. Here, we demonstrate coherent guiding of ground-state superpositions of 85Rb atoms over a centimeter range and hundreds of milliseconds inside a hollow-core photonic crystal fiber. The decoherence is mainly due to dephasing from residual differential light shift (DLS) from the optical trap and the inhomogeneity of ambient magnetic field. Our experiment establishes an important step towards a versatile platform that can lead to applications in quantum information networks and matter wave circuit for quantum sensing., Comment: Accepted by Physical Review Letters

Coherent interactions between electromagnetic and matter waves lie at the heart of quantum science and technology. However, the diffraction nature of light has limited the scalability of many atom-light based quantum systems. Here, we use the optical fields in a hollow-core photonic crystal fiber to spatially split, reflect, and recombine a coherent superposition state of free-falling 85Rb atoms to realize an inertia-sensitive atom interferometer. The interferometer operates over a diffraction-free distance, and the contrasts and phase shifts at different distances agree within one standard error. The integration of phase coherent photonic and quantum systems here shows great promise to advance the capability of atom interferometers in the field of precision measurement and quantum sensing with miniature design of apparatus and high efficiency of laser power consumption.

We theoretically study a superradiant laser, deriving both the steady-state behaviors and small-amplitude responses of the laser's atomic inversion, atomic polarization, and light field amplitude. Our minimum model for a three-level laser includes atomic population accumulating outside of the lasing transition and dynamics of the atomic population distribution causing cavity frequency tuning, as can occur in realistic experimental systems. We show that the population dynamics can act as real-time feedback to stabilize or de-stabilize the laser's output power, and we derive the cavity frequency tuning for a Raman laser. We extend the minimal model to describe a cold-atom Raman laser using $^{87}$Rb, showing that the minimal model qualitatively captures the essential features of the more complex system. This work informs our understanding of the stability of proposed millihertz linewidth lasers based on ultranarrow optical atomic transitions and will guide the design and development of these next-generation optical frequency references., Comment: 18 pages, 20 Figures, 5 page appendix

Collective measurements can project a system into an entangled state with enhanced sensitivity for measuring a quantum phase, but measurement back-action has limited previous efforts to only modest improvements. Here we use a collective measurement to produce and directly observe, with no background subtraction, an entangled, spin-squeezed state with phase resolution improved in variance by a factor of 10.5(1.5), or 10.2(6) dB, compared to the initially unentangled ensemble of N = 4.8 x 10^5 87Rb atoms. The measurement uses a cavity-enhanced probe of an optical cycling transition to mitigate back-action associated with state-changing transitions induced by the probe. This work establishes collective measurements as a powerful technique for generating entanglement for precision measurement, with potential impacts in biological sensing, communication, navigation, and tests of fundamental physics., Comment: 9 figures, 1 table

Probing the collective spin state of an ensemble of atoms may provide a means to reduce heating via the photon recoil associated with the measurement and provide a robust, scalable route for preparing highly entangled states with spectroscopic sensitivity below the standard quantum limit for coherent spin states. The collective probing relies on obtaining a very large optical depth that can be effectively increased by placing the ensemble within an optical cavity such that the probe light passes many times through the ensemble. Here we provide expressions for measurement resolution and spectroscopic enhancement in such cavity-aided non-demolition measurements as a function of cavity detuning. In particular, fundamental limits on spectroscopic enhancements in $^{87}$Rb are considered., Comment: Substantially shortened. 19 pages, 16 figures

We demonstrate a proof-of-principle magnetometer that relies on the active oscillation of a cold atom Raman laser to continuously map a field-sensitive atomic phase onto the phase of the radiated light. We demonstrate wideband sensitivity during continuous active oscillation, as well as narrowband sensitivity in passive Ramsey-like mode with translation of the narrowband detection in frequency using spin-echo techniques. The sensor operates with a sensitivity of 190 pT/Hz^(1/2) at 1 kHz and effective sensing volume of 2 * 10^-3 mm^3. Fundamental quantum limits on the magnetic field sensitivity of an ideal detector are also considered., Comment: 5 pages, 4 figures

We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled $^{87}$Rb Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the role of cavity feedback on stabilizing or enhancing relaxation oscillations. This experimental study of the stability of an optical laser operating deep into the bad-cavity regime will guide future development of superradiant lasers with ultranarrow linewidths., Comment: 9 pages, 6 figures

We implement dynamic control of a superradiant, cold atom $^{87}$Rb Raman laser to realize the equivalent of conditional Ramsey spectroscopy for sensing atomic phase shifts. Our method uses the non-demolition mapping of the collective quantum phase of an ensemble of two-level atoms onto the phase of a detected cavity light field. We show that the fundamental precision of the non-demolition measurement can theoretically approach the standard quantum limit on phase estimation for a coherent spin state, the traditional benchmark for Ramsey spectroscopy. Finally, we propose a hybrid optical lattice clock based on this method that combines continuous and discrete measurements to realize both high precision and accuracy., Comment: 7 pages, 4 figures

We describe and characterize a simple, low cost, low phase noise microwave source that operates near 6.800 GHz for agile, coherent manipulation of ensembles of 87Rb. Low phase noise is achieved by directly multiplying a low phase noise 100 MHz crystal to 6.8 GHz using a non-linear transmission line and filtering the output with custom band-pass filters. The fixed frequency signal is single sideband modulated with a direct digital synthesis frequency source to provide the desired phase, amplitude, and frequency control. Before modulation, the source has a single sideband phase noise near -140 dBc/Hz in the range of 10 kHz to 1 MHz offset from the carrier frequency and -130 dBc/Hz after modulation. The resulting source is estimated to contribute added spin-noise variance 16 dB below the quantum projection noise level during quantum nondemolition measurements of the clock transition in an ensemble 7x10^5 87Rb atoms., Comment: 5 pages, 3 figures

We use the vacuum Rabi splitting to perform quantum nondemolition (QND) measurements that prepare a conditionally spin-squeezed state of a collective atomic psuedo-spin. We infer a 3.4(6) dB improvement in quantum phase estimation relative to the standard quantum limit for a coherent spin state composed of uncorrelated atoms. The measured collective spin is composed of the two-level clock states of nearly 10^6 Rb-87 atoms confined inside a low finesse F = 710 optical cavity. This technique may improve atomic sensor precision and/or bandwidth, and may lead to more precise tests of fundamental physics., Comment: Letter (4 pages, 4 figures) and Supporting Material (3 pages). To appear in Phys. Rev. Lett