Distributed quantum sensing with mode-entangled spin-squeezed atomic states.

Quantum sensors are used for precision timekeeping, field sensing and quantum communication1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.

Measurement noise 100 times lower than the quantum-projection limit using entangled atoms.

Quantum metrology uses quantum entanglement--correlations in the properties of microscopic systems--to improve the statistical precision of physical measurements. When measuring a signal, such as the phase shift of a light beam or an atomic state, a prominent limitation to achievable precision arises from the noise associated with the counting of uncorrelated probe particles. This noise, commonly referred to as shot noise or projection noise, gives rise to the standard quantum limit (SQL) to phase resolution. However, it can be mitigated down to the fundamental Heisenberg limit by entangling the probe particles. Despite considerable experimental progress in a variety of physical systems, a question that persists is whether these methods can achieve performance levels that compare favourably with optimized conventional (non-entangled) systems. Here we demonstrate an approach that achieves unprecedented levels of metrological improvement using half a million (87)Rb atoms in their 'clock' states. The ensemble is 20.1 ± 0.3 decibels (100-fold) spin-squeezed via an optical-cavity-based measurement. We directly resolve small microwave-induced rotations 18.5 ± 0.3 decibels (70-fold) beyond the SQL. The single-shot phase resolution of 147 microradians achieved by the apparatus is better than that achieved by the best engineered cold atom sensors despite lower atom numbers. We infer entanglement of more than 680 ± 35 particles in the atomic ensemble. Applications include atomic clocks, inertial sensors, and fundamental physics experiments such as tests of general relativity or searches for electron electric dipole moment. To this end, we demonstrate an atomic clock measurement with a quantum enhancement of 10.5 ± 0.3 decibels (11-fold), limited by the phase noise of our microwave source.

40 W, 780 nm laser system with compensated dual beam splitters for atom interferometry.

We demonstrate a narrow-linewidth 780 nm laser system with up to 40W power and a frequency modulation bandwidth of 230 MHz. Efficient overlap on nonlinear optical elements combines two pairs of phase-locked frequency components into a single beam. Serrodyne modulation with a high-quality sawtooth waveform is used to perform frequency shifts with >96.5% efficiency over tens of megahertz. This system enables next-generation atom interferometry by delivering simultaneous, Stark-shift-compensated dual beam splitters while minimizing spontaneous emission.

Atom-Interferometric Test of the Equivalence Principle at the 10

We use a dual-species atom interferometer with 2 s of free-fall time to measure the relative acceleration between ^{85}Rb and ^{87}Rb wave packets in the Earth's gravitational field. Systematic errors arising from kinematic differences between the isotopes are suppressed by calibrating the angles and frequencies of the interferometry beams. We find an Eötvös parameter of η=[1.6±1.8(stat)±3.4(syst)]×10^{-12}, consistent with zero violation of the equivalence principle. With a resolution of up to 1.4×10^{-11} g per shot, we demonstrate a sensitivity to η of 5.4×10^{-11}/sqrt[Hz].

Free Space Ramsey Spectroscopy in Rubidium with Noise below the Quantum Projection Limit.

We demonstrate the utility of optical cavity generated spin-squeezed states in free space atomic fountain clocks in ensembles of 390 000 ^{87}Rb atoms. Fluorescence imaging, correlated to an initial quantum nondemolition measurement, is used for population spectroscopy after the atoms are released from a confining lattice. For a free fall time of 4 milliseconds, we resolve a single-shot phase sensitivity of 814(61) microradians, which is 5.8(0.6) decibels (dB) below the quantum projection limit. We observe that this squeezing is preserved as the cloud expands to a roughly 200 µm radius and falls roughly 300 µm in free space. Ramsey spectroscopy with 240 000 atoms at a 3.6 ms Ramsey time results in a single-shot fractional frequency stability of 8.4(0.2)×10^{-12}, 3.8(0.2) dB below the quantum projection limit. The sensitivity and stability are limited by the technical noise in the fluorescence detection protocol and the microwave system, respectively.

Effective Inertial Frame in an Atom Interferometric Test of the Equivalence Principle.

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.

Bell Correlations in Spin-Squeezed States of 500 000 Atoms.

Bell correlations, indicating nonlocality in composite quantum systems, were until recently only seen in small systems. Here, we demonstrate Bell correlations in squeezed states of 5×10^{5} ^{87}Rb atoms. The correlations are inferred using collective measurements as witnesses and are statistically significant to 124 standard deviations. The states are both generated and characterized using optical-cavity aided measurements.

Phase Shift in an Atom Interferometer due to Spacetime Curvature across its Wave Function.

Spacetime curvature induces tidal forces on the wave function of a single quantum system. Using a dual light-pulse atom interferometer, we measure a phase shift associated with such tidal forces. The macroscopic spatial superposition state in each interferometer (extending over 16 cm) acts as a nonlocal probe of the spacetime manifold. Additionally, we utilize the dual atom interferometer as a gradiometer for precise gravitational measurements.

Iterative creation and sensing of twisted light.

The iterative interaction of a photon with a sample can lead to increased sensitivity in measuring the properties of the samples, such as its refractive index or birefringence. Here we show that this principle can also be used to generate and sense states of light. In particular, we demonstrate a technique to generate states with high orbital angular momentum using a single-vortex phase plate (VPP). This is accomplished by placing the phase plate in a self-imaging cavity such that light interacts with it multiple times; for an ideal phase plate, this is equivalent to iterative applications of the angular momentum operator. Using a discrete VPP, we show that our setup realizes a high-dimensional generalization of the Pauli matrix σx, and that the created states show sub-diffraction limited features that might find applications in structured illumination microscopy.

Ultrafast oscilloscope based on laser-triggered field emitters.

Laser-triggered electron emission from sharp metal tips has been demonstrated in recent years as a high brightness, ultrafast electron source. Its possible applications range from ultrafast electron microscopy to laser-based particle accelerators to electron interferometry. The ultrafast nature of the emission process allows for the sampling of an instantaneous radio frequency (RF) voltage that has been applied to a field emitter. For proof-of-concept, we use an RF signal derived from our laser's repetition rate, mapping a 9.28 GHz signal in 22.4 fs steps with 28 mv accuracy.

Ultrafast Time-Resolved Photoelectric Emission.

The emission times of laser-triggered electrons from a sharp tungsten tip are directly characterized under ultrafast, near-infrared laser excitation at Keldysh parameters of 6.6<γ<19.1. Emission delays up to 10 fs are observed, which are inferred from the energy gain of photoelectrons emitted into a synchronously driven microwave cavity. Few femtosecond timing resolution is achieved in a configuration capable of measuring timing shifts up to 55 ps. The technique can also be used to measure the microwave phase inside the cavity with a precision below 70 fs upon the energy resolved detection of a single electron.

Matter wave lensing to picokelvin temperatures.

Using a matter wave lens and a long time of flight, we cool an ensemble of ^{87}Rb atoms in two dimensions to an effective temperature of less than 50_{-30}^{+50} pK. A short pulse of red-detuned light generates an optical dipole force that collimates the ensemble. We also report a three-dimensional magnetic lens that substantially reduces the chemical potential of evaporatively cooled ensembles with a high atom number. By observing such low temperatures, we set limits on proposed modifications to quantum mechanics in the macroscopic regime. These cooling techniques yield bright, collimated sources for precision atom interferometry.

Many-atom-cavity QED system with homogeneous atom-cavity coupling.

We demonstrate a many-atom-cavity system with a high-finesse dual-wavelength standing wave cavity in which all participating rubidium atoms are nearly identically coupled to a 780-nm cavity mode. This homogeneous coupling is enforced by a one-dimensional optical lattice formed by the field of a 1560-nm cavity mode.

New method for gravitational wave detection with atomic sensors.

Laser frequency noise is a dominant noise background for the detection of gravitational waves using long-baseline optical interferometry. Amelioration of this noise requires near simultaneous strain measurements on more than one interferometer baseline, necessitating, for example, more than two satellites for a space-based detector or two interferometer arms for a ground-based detector. We describe a new detection strategy based on recent advances in optical atomic clocks and atom interferometry which can operate at long baselines and which is immune to laser frequency noise. Laser frequency noise is suppressed because the signal arises strictly from the light propagation time between two ensembles of atoms. This new class of sensor allows sensitive gravitational wave detection with only a single baseline. This approach also has practical applications in, for example, the development of ultrasensitive gravimeters and gravity gradiometers.

Enhanced atom interferometer readout through the application of phase shear.

We present a method for determining the phase and contrast of a single shot of an atom interferometer. The application of a phase shear across the atom ensemble yields a spatially varying fringe pattern at each output port, which can be imaged directly. This method is broadly relevant to atom-interferometric precision measurement, as we demonstrate in a 10 m 87Rb atomic fountain by implementing an atom-interferometric gyrocompass with 10 mdeg precision.

Multiaxis inertial sensing with long-time point source atom interferometry.

We show that light-pulse atom interferometry with atomic point sources and spatially resolved detection enables multiaxis (two rotation, one acceleration) precision inertial sensing at long interrogation times. Using this method, we demonstrate a light-pulse atom interferometer for 87Rb with 1.4 cm peak wave packet separation and a duration of 2T=2.3 s. The inferred acceleration sensitivity of each shot is 6.7×10(-12)g, which improves on previous limits by more than 2 orders of magnitude. We also measure Earth's rotation rate with a precision of 200 nrad/s.

Wide-field fluorescence lifetime imaging of neuron spiking and subthreshold activity in vivo.

The development of voltage-sensitive fluorescent probes suggests fluorescence lifetime as a promising readout for electrical activity in biological systems. Existing approaches fail to achieve the speed and sensitivity required for voltage imaging in neuroscience applications. We demonstrated that wide-field electro-optic fluorescence lifetime imaging microscopy (EO-FLIM) allows lifetime imaging at kilohertz frame-acquisition rates, spatially resolving action potential propagation and subthreshold neural activity in live adult Drosophila. Lifetime resolutions of <5 picoseconds at 1 kilohertz were achieved for single-cell voltage recordings. Lifetime readout is limited by photon shot noise, and the method provides strong rejection of motion artifacts and technical noise sources. Recordings revealed local transmembrane depolarizations, two types of spikes with distinct fluorescence lifetimes, and phase locking of spikes to an external mechanical stimulus.

Generation of 43 W of quasi-continuous 780 nm laser light via high-efficiency, single-pass frequency doubling in periodically poled lithium niobate crystals.

We demonstrate high-efficiency frequency doubling of the combined output of two 1560 nm 30 W fiber amplifiers via single pass through periodically poled lithium niobate (PPLN) crystals. The temporal profile of the 780 nm output is controlled by adjusting the relative phase between the seeds of the amplifiers. We obtain a peak power of 34 W of 780 nm light by passing the combined output through one PPLN crystal, and a peak power of 43 W by passing through two cascading PPLN crystals. This source provides high optical power, excellent beam quality and spectral purity, and agile frequency and amplitude control in a simple and compact setup, which is ideal for applications such as atom optics using Rb atoms.

Observation of a gravitational Aharonov-Bohm effect.

Gravity curves space and time. This can lead to proper time differences between freely falling, nonlocal trajectories. A spatial superposition of a massive particle is predicted to be sensitive to this effect. We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg's error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.