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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 propose a multilayer device comprising of a thin-film-based ferromagnetic hetero-structure (FMH) deposited on a diamond layer doped with nitrogen vacancy centers (NVC's). We find that when the NVC's are in close proximity (1-2 nm) with the FMH, the exchange energy is comparable to, and may even surpass the magnetostatic interaction energy. This calls for the need to consider and utilize both effects in magnetometry based on NVC's in diamond. As the distance between the FMH and NVC is decreased to the sub-nanometer scale, the exponential increase in the exchange energy suggests spintronic applications of NVC beyond magnetometry, such as detection of spin-Hall effect or spin currents., Comment: 10 pages, 6 figures

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

Quantum manipulation protocols for quantum sensors and quantum computation often require many single qubit rotations. However, the impact of phase noise in the field that performs the qubit rotations is often neglected or treated only for special cases. We present a general framework for calculating the impact of phase noise on the state of a qubit, as described by its equivalent Bloch vector. The analysis applies to any Bloch vector orientation, and any rotation axis azimuthal angle for both a single pulse, and pulse sequences. Experimental examples are presented for several special cases. We apply the analysis to commonly used composite $\pi$-pulse sequences: CORPSE, SCROFULOUS, and BB1, used to suppress static amplitude and detuning errors, and also to spin echo sequences. We expect the formalism presented will help guide the development and evaluation of future quantum manipulation protocols., Comment: 12 pages, 6 figures, submitted to PRA

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