Mach-Zehnder Atom Interferometer Research Articles

Raman transitions driven by phase-modulated light in a cavity atom interferometer

Atom interferometers in optical cavities benefit from strong laser intensities and high-quality wavefronts. The laser frequency pairs that are needed for driving Raman transitions (often generated by phase modulating a monochromatic beam) form multiple standing waves in the cavity, resulting in a periodic spatial variation of the properties of the atom-light interaction along the cavity axis. Here, we model this spatial dependence and calculate two-photon Rabi frequencies and ac Stark shifts. We compare the model to measurements performed with varying cavity and pulse parameters such as cavity offset from the carrier frequency and the longitudinal position of the atom cloud. We show how setting cavity parameters to optimal values can increase the Raman transition efficiency at all positions in the cavity and nearly double the contrast in a Mach-Zehnder cavity atom interferometer in comparison to the unoptimized case.

Self-alignment of a large-area dual-atom-interferometer gyroscope using parameter-decoupled phase-seeking calibrations

We report a Mach-Zehnder-type dual-atom-interferometer gyroscope with an interrogation arm of 40-cm length and the interference area up to $1.2\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}$. The precise angular alignment of the large-scale separated Raman lasers is demonstrated by seeking the phase intersection of Ramsey-$\mathrm{Bord}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}$ interferometers after the gravity effect is compensated and by decoupling the velocity dependent cross-talk phase shifts, and applied to build the Mach-Zehnder atom interferometer. Then a compact inertial rotation sensor is realized based on dual large-area Mach-Zehnder atom interferometers by precisely aligning the large-scale separated Raman lasers, in which the coherence is well preserved and the common noise is differentially suppressed. The sensor presents a sensitivity of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ $\mathrm{rad}/\mathrm{s}/{\mathrm{Hz}}^{1/2}$, and a stability of $9.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\mathrm{s}$ at 23000 s. The absolute rotation measurement is carried out by adjusting the atomic velocity which corresponds to modulating the scale factor.

Optimal control of Raman pulse sequences for atom interferometry

We present the theoretical design and experimental implementation of mirror and beamsplitter pulses that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These pulses are designed using the GRAPE optimal control algorithm and demonstrated experimentally with a cold thermal sample of 85Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional π pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the π pulse fidelity is below 20%, and is thus suitable for large momentum transfer interferometers using thermal atoms or operating in non-ideal environments. We then extend our optimization to all components of a Mach–Zehnder atom interferometer sequence and show that with a highly inhomogeneous atomic sample the fringe visibility is increased threefold over that using conventional π and π/2 pulses.

Zero-velocity atom interferometry using a retroreflected frequency-chirped laser

Atom interferometry using stimulated Raman transitions in a retroreflected configuration is the first choice in high precision measurements because it provides low phase noise, high quality Raman wavefront and simple experimental setup. However, it cannot be used for atoms at zero velocity because two pairs of Raman lasers are simultaneously resonant. Here we report a method which allows to lift this degeneracy by using a frequency chirp on the Raman lasers. Using this technique, we realize a Mach-Zehnder atom interferometer hybridized with a force balanced accelerometer which provides horizontal acceleration measurements with a short-term sensitivity of $3.2\times 10^{-5}$ m.s$^{-2}$/$\sqrt{Hz}$. We check at the level of precision of our experiment the absence of bias induced by this method. This technique could be used for multiaxis inertial sensors, tiltmeters or atom interferometry in a microgravity environment.

Proper time in atom interferometers: Diffractive versus specular mirrors

We compare a conventional Mach-Zehnder light-pulse atom interferometer based on diffractive mirrors with one that uses specular reflection. In contrast to diffractive mirrors that generate a symmetric configuration, specular mirrors realized, for example, by evanescent fields lead under the influence of gravity to an asymmetric geometry. In such an arrangement the interferometer phase contains nonrelativistic signatures of proper time.

Optimal control of mirror pulses for cold-atom interferometry

Atom matterwave interferometry requires mirror and beamsplitter pulses that are robust to inhomogeneities in field intensity, magnetic environment, atom velocity and Zeeman sub-state. Pulse shapes determined using quantum control methods offer significantly improved interferometer performance by allowing broader atom distributions, larger interferometer areas and higher contrast. We have applied gradient ascent pulse engineering (GRAPE) to optimise the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when averaged over atoms with an experimentally relevant range of velocities, beam intensities, and Zeeman states. Pulses were found to be highly robust to variations in detuning and coupling strength, and offer a clear improvement in robustness over the best established composite pulses. The peak mirror fidelity in a cloud of $\sim 80\ \mu$K ${}^{85}$Rb atoms is predicted to be improved by a factor of 2 compared with standard rectangular $\pi$ pulses.

Competition effects of multiple quantum paths in an atom interferometer

We present an observation of competition effect among multiple quantum paths in a Raman-type Mach-Zehnder atom interferometer. By measuring the contrast of interference fringes, the competition effect among multiple interference paths is experimentally investigated. Due to the phase competition, the contrast periodically oscillates when modulating either the phase or the interrogation time between Raman pulses. The multiple quantum paths form because of the imperfect population transfer efficiency in stimulated Raman transitions, and are verified by modulating the duration of Raman pulses. The contrast could be optimized by suppressing the phase competition.

Low-phase noise and high-power laser for Bragg atom interferometer

We present a laser system with low-phase noise and an output power up to 8.8 W at 780 nm for driving Bragg transitions in a 87Rb fountain. An optical phase-locked loop (OPLL) is employed to restrain the phase noise that arises from the spatial separation of the two Bragg beams at low frequencies. The residual phase variance is suppressed by two orders around 400 Hz. A Mach-Zehnder Bragg atom interferometer, based on the four-photon recoil scheme, has been realized using this laser system. This interferometer shows a resolution of 5×10−9g at an integration time of 1200 s for gravity measurements.

Simultaneous Precision Gravimetry and Magnetic Gradiometry with a Bose-Einstein Condensate: A High Precision, Quantum Sensor.

A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A 5×10^{6} atom F=1 spinor condensate of ^{87}Rb is released into free fall for up to 750ms and probed with a T=130 ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states |m_{f}=1,0,-1⟩, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of Δg/g=1.45×10^{-9} and the magnetic field gradient to a precision of 120 pT/m.

A Bose-condensed, simultaneous dual-species Mach–Zehnder atom interferometer

This paper presents the first realization of a simultaneous 87Rb–85Rb Mach–Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the weak equivalence principle rely on such a system. This implementation utilizes hybrid magnetic-optical trapping to produce spatially overlapped condensates with a repetition rate of 20 s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non–linear phase shift on a non-interacting 85Rb interferometer as a function of interferometer time, T, which we show arises from inter-isotope scattering with the co-incident 85Rb interferometer. A discussion of implications for future experiments is given.

PRINCIPLES OF GRAVITATIONAL WAVES DETECTION THROUGH ATOM INTERFEROMETRY

The output of a simple Mach-Zehnder atom interferometer (with light field beam splitters) is studied in order to obtain sensitivity curves for GW signals in the paraxial approximation by using the ABCD matrices techniques and first order perturbation theory for mirroratom interaction; order of magnitude of relevant physical parameters for a realistic GW detector through atom interferometry is deduced, both for single- and coupled-interferometers configurations. Finally a synthetic overview of ongoing activities of the Florence-Urbino group in this field is presented.

Optimal Gaussian squeezed states for atom interferometry in the presence of phase diffusion

We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states, in the presence interactions. For weak interactions, our results coincide with Phys. Rev. Lett. {\bf 100}, 250406 (2008), with optimal initial number-variance $\sigma_o\propto N^{1/3}$ and optimal signal-to-noise ratio $s_o\propto N^{2/3}$ for total atom number $N$. As the interaction strength $u$ increases past unity, phase-diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number-squeezing to initial {\it phase}-squeezing with $\sigma_o\propto\sqrt{uN}$ and $s_o\propto\sqrt{N/u}$ shot-noise scaling. The initial phase-squeezing translates into hold-time number-squeezing, which is less sensitive to interactions than coherent states and improves $s_o$ by a factor of $\sqrt{u}$.

Absolute and ratio measurements of the polarizability of Na, K, and Rb with an atom interferometer

We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find ${\ensuremath{\alpha}}_{\mathrm{Na}}=24.11(2){}_{\mathrm{stat}}(18){}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}{\mathrm{cm}}^{3}$, ${\ensuremath{\alpha}}_{\mathrm{K}}=43.06(14)(33)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(12)(42)$. Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with $0.3%$ uncertainty. We find ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.959(5)$, ${\ensuremath{\alpha}}_{\mathrm{K}}/{\ensuremath{\alpha}}_{\mathrm{Na}}=1.786(6)$, and ${\ensuremath{\alpha}}_{\mathrm{Rb}}/{\ensuremath{\alpha}}_{\mathrm{K}}=1.097(5)$. We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find ${\ensuremath{\alpha}}_{\mathrm{K}}=43.06(21)$ and ${\ensuremath{\alpha}}_{\mathrm{Rb}}=47.24(21)$.

Atom-Interferometry Tests of the Isotropy of Post-Newtonian Gravity

We present a test of the local Lorentz invariance of post-Newtonian gravity by monitoring Earth's gravity with a Mach-Zehnder atom interferometer that features a resolution of up to 8 x 10{-9}g/sqrt[Hz], the highest reported thus far. Expressed within the standard model extension (SME) or Nordtvedt's anisotropic universe model, the analysis limits four coefficients describing anisotropic gravity at the ppb level and three others, for the first time, at the 10 ppm level. Using the SME we explicitly demonstrate how the experiment actually compares the isotropy of gravity and electromagnetism.

Measurement of the refraction index for atom waves

We have developed a Mach-Zehnder atom interferometer which uses elastic diffraction of lithium atom on laser standing waves for the coherent manipulation of the atom wave. The interference signal is of sufficient quality to achieve a phase sensitivity near 10 milliradians/√Hz. With this apparatus, we have recently measured the index of refraction of several gases for lithium waves. The interference signals give access to the real and imaginary parts of (n - 1) and we have tested the linear dependence of these two quantities with gas density. The measured values of (n-1) are in good agreement with calculations and they exhibit glory oscillations, as predicted by theory.

Vibration-induced phase noise in Mach–Zehnder atom interferometers

The high inertial sensitivity of atom interferometers has been used to build accelerometers and gyrometers but this sensitivity makes these interferometers very sensitive to the laboratory seismic noise. This seismic noise induces a phase noise which is large enough to reduce the fringe visibility in many cases. We develop here a model calculation of this phase noise in the case of Mach-Zehnder atom interferometers and we apply this model to our thermal lithium interferometer. We are thus able to explain the observed dependence of the fringe visibility with the diffraction order. The dynamical model developed in the present paper should be very useful to further reduce this phase noise in atom interferometers and this reduction should open the way to improved interferometers.

Measurement of atomic diffraction phases induced by material gratings

Atom-surface interactions can significantly modify the intensity and phase of atom de Broglie waves diffracted by a silicon nitride grating. This affects the operation of a material grating as a coherent beam splitter. The phase shifts induced by diffraction are measured by comparing the relative phases of several interfering paths in a Mach-Zehnder Na atom interferometer formed by three material gratings. The values of the diffraction phases are consistent with a simple model which includes a van der Waals atom-surface interaction between the Na atoms and the silicon nitride grating bars.

Matter-Wave Decoherence due to a Gas Environment in an Atom Interferometer

Decoherence due to scattering from background gas particles is observed for the first time in a Mach-Zehnder atom interferometer, and compared with decoherence due to scattering photons. A single theory is shown to describe decoherence due to scattering either atoms or photons. Predictions from this theory are tested by experiments with different species of background gas, and also by experiments with different collimation restrictions on an atom beam interferometer.

Noise limits in matter-wave interferometry using degenerate quantum gases

We analyze the phase resolution limit of a Mach-Zehnder atom interferometer whose input consists of degenerate quantum gases of either bosons or fermions. For degenerate gases, the number of atoms within one de Broglie wavelength is larger than unity, so that atom-atom interactions and quantum statistics are no longer negligible. We show that for equal atom numbers, the phase resolution achievable with fermions is noticeably better than for interacting bosons.

Some theoretical and experimental aspects of three-grating Mach–Zehnder atom interferometers

In this contribution, we present some recent theoretical results concerning the fringe contrast in Mach–Zehnder atom interferometers and the use of Bloch states to describe atomic diffraction. We also describe the observation of diffraction of lithium at thermal energy by a quasi-resonant laser standing wave.