The quantum superposition principle allows massive particles to be delocalized over distant positions. Though quantum mechanics has proved adept at describing the microscopic world, quantum superposition runs counter to intuitive conceptions of reality and locality when extended to the macroscopic scale, as exemplified by the thought experiment of Schrödinger's cat. Matter-wave interferometers, which split and recombine wave packets in order to observe interference, provide a way to probe the superposition principle on macroscopic scales and explore the transition to classical physics. In such experiments, large wave-packet separation is impeded by the need for long interaction times and large momentum beam splitters, which cause susceptibility to dephasing and decoherence. Here we use light-pulse atom interferometry to realize quantum interference with wave packets separated by up to 54 centimetres on a timescale of 1 second. These results push quantum superposition into a new macroscopic regime, demonstrating that quantum superposition remains possible at the distances and timescales of everyday life. The sub-nanokelvin temperatures of the atoms and a compensation of transverse optical forces enable a large separation while maintaining an interference contrast of 28 per cent. In addition to testing the superposition principle in a new regime, large quantum superposition states are vital to exploring gravity with atom interferometers in greater detail. We anticipate that these states could be used to increase sensitivity in tests of the equivalence principle, measure the gravitational Aharonov-Bohm effect, and eventually detect gravitational waves and phase shifts associated with general relativity.

We show that light-pulse atom interferometry with atomic point sources and spatially resolved detection enables multi-axis (two rotation, one acceleration) precision inertial sensing at long interrogation times. Using this method, we demonstrate a light-pulse atom interferometer for 87 Rb with 1.4 cm peak wavepacket separation and a duration of 2 T = 2.3 s. The inferred acceleration sensitivity of each shot is 6.7 × 10 −12 g, which improves on previous limits by more than two orders of magnitude. We also measure the Earth's rotation rate with a precision of 200 nrad/s.PACS numbers: 03.75. Dg, 37.25.+k, 06.30.Gv Light-pulse atom interferometry enables precision tests of gravity [1][2][3] and electrodynamics [4] as well as practical applications in inertial navigation, geodesy, and timekeeping. Phase shifts for light-pulse atom interferometers demonstrate sensitivity to the initial velocity distribution of the atom source, often resulting in inhomogeneous dephasing that washes out fringe contrast [5]. In this Letter, we show that use of spatially resolved imaging in combination with an initially spatially localized atomic source allows direct characterization of these phase shifts. We refer to this technique as point source interferometry (PSI).The contrast loss associated with such inhomogeneous dephasing is not fundamental, but is a consequence of atom detection protocols that average over velocitydependent phase shifts. With PSI we establish a correlation between velocity and position and use spatiallyresolved detection to form an image of the ensemble that reveals its velocity-dependent phase structure. A simple way to realize this correlation is through ballistic expansion of the ensemble. In the limit that the ensemble size at detection is much larger than its initial size, each atom's position is approximately proportional to its initial velocity. Consequently, any initial velocitydependent phase shift results in a spatial variation of the interferometer phase, yielding a position-dependent population difference between the two output ports of the interferometer.An important example of velocity sensitivity is due to rotation of the interferometer laser beams [3,6]. Rotation at a rate Ω leads to a phase shift (Table I, term 2) that depends on (v x , v y ), the initial transverse velocity of the atom. In a rotating frame, this effect may be interpreted as a Coriolis acceleration. PSI also allows observation of longitudinal velocity-dependent phase shifts in asymmetric atom interferometers [7] (e.g., Table I, term 3).To demonstrate PSI, we induce a velocity-dependent phase shift in a 87 Rb Raman light-pulse atom interferometer. We launch cold atoms from the bottom of a 10-meter tall vacuum enclosure (Fig. 1a) and apply a threepulse accelerometer sequence (π/2−π−π/2) [8]. The first pulse serves as an atom beamsplitter, coherently driving the atoms into a superposition of states |F = 1; p and |F = 2; p + k eff with momentum difference k eff = 2 k. Over the subsequent T = 1.15 s interrogation interval, the two...

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 +50 −30 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 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.

We propose an atom interferometer gravitational wave detector in low Earth orbit (AGIS-LEO). Gravitational waves can be observed by comparing a pair of atom interferometers separated by a 30 km baseline. In the proposed configuration, one or three of these interferometer pairs are simultaneously operated through the use of two or three satellites in formation flight. The three satellite configuration allows for the increased suppression of multiple noise sources and for the detection of stochastic gravitational wave signals. The mission will offer a strain sensitivity of < 10 −18 / √ Hz in the 50 mHz-10 Hz frequency range, providing access to a rich scientific region with 123 1954 J. M. Hogan et al. substantial discovery potential. This band is not currently addressed with the LIGO, VIRGO, or LISA instruments. We analyze systematic backgrounds that are relevant to the mission and discuss how they can be mitigated at the required levels. Some of these effects do not appear to have been considered previously in the context of atom interferometry, and we therefore expect that our analysis will be broadly relevant to atom interferometric precision measurements. Finally, we present a brief conceptual overview of shorter-baseline ( 100 m) atom interferometer configurations that could be deployed as proof-of-principle instruments on the International Space Station (AGIS-ISS) or an independent satellite.

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 87 Rb atomic fountain by implementing an atom interferometric gyrocompass with 10 millidegree precision.PACS numbers: 03.75. Dg, 37.25.+k, 06.30.Gv Light-pulse atom interferometers use short optical pulses to split, redirect, and interfere freely-falling atoms [1]. They have proven widely useful for precision metrology. Atom interferometers have been employed in measurements of the gravitational [2, 3] and fine-structure [4] constants, in on-going laboratory tests of the equivalence principal [5] and general relativity [6,7], and have been proposed for use in gravitational wave detection [8,9]. They have also enabled the realization of high performance gyroscopes [10], accelerometers [11], gravimeters [12], and gravity gradiometers [13].Current-generation light-pulse atom interferometers determine phase shifts by recording atomic transition probabilities [1]. These are inferred from the populations of the two atomic states that comprise the interferometer output ports. Due to experimental imperfections, interference contrast is not perfect -even at the extremes, the dark port does not have perfect extinction. This results in the need to independently characterize contrast prior to inferring phase. Typically, this is done with a sequence of multiple shots with different phases, such that the population ratio is scanned through the contrast envelope [14]. Such an experimental protocol relies on the stability of the contrast envelope. In many cases, the contrast varies from shot to shot, introducing additional noise and bias in the phase extraction process.We present a broadly applicable technique that is capable of resolving interference phase on a single experimental shot. This is accomplished through the introduction of a phase shear across the spatial extent of the detected atom ensemble. The shear is manifest in a spatial variation of the atomic transition probability, which, under appropriate conditions, can be directly observed in an image of the cloud [ Fig. 1(b)]. Using this phase shear readout (PSR), it is no longer necessary to vary the phase over many shots to determine the contrast envelope. Instead, the contrast of each shot can be inferred from the depth of modulation of the spatial fringe pattern on the atom ensemble. The interferometer phase is directly determined from the phase of the spatial fringe.The analysis of PSR fringes reveals rich details about atom interferometer phase shifts and systematic effects, much as the analysis of a spatially varying optical in- Once they fall back to the bottom, the wavepackets are overlapped and an interference pattern (blue fringes) is imaged by two perpendicular cameras (CCD1,2). An additional optical...

We built an ultra-low-noise angle sensor by combining a folded optical lever and a Sagnac interferometer. The instrument has a measured noise floor of 1.3 prad/√Hz at 2.4 kHz. We achieve this record angle sensitivity using a proof-of-concept apparatus with a conservative N=11 bounces in the optical lever. This technique could be extended to reach subpicoradian/√Hz sensitivities with an optimized design.

We have demonstrated a 100-fold improvement in the magnetic field uniformity on the axis of a large aspect ratio, cylindrical, mumetal magnetic shield by reducing discontinuities in the material of the shield through the welding and re-annealing of a segmented shield. The three-layer shield reduces Earth's magnetic field along an 8 m region to 420 μG (rms) in the axial direction, and 460 and 730 μG (rms) in the two transverse directions. Each cylindrical shield is a continuous welded tube which has been annealed after manufacture and degaussed in the apparatus. We present both experiments and finite element analysis that show the importance of uniform shield material for large aspect ratio shields, favoring a welded design over a segmented design. In addition, we present finite element results demonstrating the smoothing of spatial variations in the applied magnetic field by cylindrical magnetic shields. Such homogenization is a potentially useful feature for precision atom interferometric measurements.

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