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 property 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 applicable to a wide class 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 on 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. PACS 03.75.Dg; 39.20.+q; 42.50.Vk     

Shot noise in Fabry-Perot interferometers based on carbon nanotubes

We report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interference, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively and allows us to determine directly the transmissions of the two channels characterizing the nanotube. In the weak backscattering regime, the dependence of the noise on the backscattering current is found weaker than expected, pointing either to electron-electron interactions or to weak decoherence.     

Broken unitarity and phase measurements in Aharonov-Bohm interferometers

Aharonov-Bohm mesoscopic solid-state interferometers yield a conductance which contains a term cos(phi+beta), where phi relates to the magnetic flux. Experiments with a quantum dot on one of the interfering paths aim to relate beta to the dot's intrinsic Friedel transmission phase alpha(1). For closed systems, which conserve the electron current (unitarity), the Onsager relation requires that beta = 0 or pi. For open systems, we show that in general beta depends on the details of the broken unitarity. Although it gives information on the resonances of the dot, beta is generally not equal to alpha(1). A direct relation between beta and alpha(1) requires specific ways of opening the system, which are discussed.     

Thermal noise computation in gravitational wave interferometers from first principles

We propose a universal method of computation of thermal noise in mirrors of gravitational wave interferometers based on first principles. We imagine a situation where a mirror is part of a Fabry–Perot cavity. The movement of the mirror's surface produces variation of the eigen frequency of the cavity, which is computed by evaluating the variation of the energy stored in cavity. We consider two particular examples: first, the thermal noise from a dielectric slab inside the Fabry–Perot cavity, and second, the polarization-dependent thermal noise in the folded cavity.     

Spectrum control and shaping of optical pulses in optical fibre interferometers

This paper discusses the use of single-mode fibre ring interferometers for injection laser line narrowing and for enhancement of optical emission power. The efficient launching into fibre ring interferometers of multi-frequency external cavity injection laser emission, in both the c.w. and mode-locking regime, has been achieved. Matching the optical lengths of the external cavity and fibre interferometer allowed the measurement of mode width of such a laser. A method is proposed for shaping optical pulses in fibre ring interferometers from constant intensity frequency modulated emission. The mode-locking regime of all-fibre external cavity injection lasers has been achieved.     

Reduction of quantum noise in optical interferometers using squeezed light

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25, 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.     

Analysis of the phase lapse problem in closed interferometers

We investigate the connection between the asymmetry of the Fano resonances in a mesoscopic interferometer with an embedded quantum dot and the π lapses in the phase of the “bare” dot transmittance. Consecutive Fano resonances with the same (opposite) sign of the Fano parameter imply the presence (absence) of a phase lapse with π between the corresponding resonances of the dot. Our results suggest that the famous “phase lapse” problem, first reported by Schuster et al. [R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H. Shtrikman, Nature 385 (1997) 417], can therefore be experimentally addressed in closed interferometers. It is also proposed that the Fano effect can be used to extract the phase distributions of the eigenfunctions for a mesoscopic 2D shape, via the parity of the resonances. In the presence of electron–electron interaction, one can calculate the phases of the T-matrix elements. The numerical results lead to the same conclusions as for the non-interacting case.     

High-order inertial phase shifts for time-domain atom interferometers

High-order inertial phase shifts are calculated for time-domain atom interferometers. We obtain closed-form analytic expressions for these shifts in accelerometer, gyroscope, optical clock and photon recoil measurement configurations. Our analysis includes Coriolis, centrifugal, gravitational, and gravity gradient-induced forces. We identify new shifts which arise at levels relevant to current and planned experiments. PACS 39.20.+Q; 32.80.Pj; 03.75.Dg; 04.80.-Y     

High-resolution frequency estimation technique for recovering phase distribution in interferometers

An integral approach to phase measurement is presented. First, the use of a high-resolution technique for the pixelwise detection of phase steps is proposed. Next, the robustness of the algorithm that is developed is improved by incorporation of a denoising procedure during spectral estimation. The pixelwise knowledge of phase steps is then applied to the Vandermonde system of equations for retrieval of phase values at each pixel point. Conceptually, our proposal involves the design of an annihilating filter that has zeros at the frequencies associated with the polynomial that describes the fringe intensity. The parametric estimation of this annihilating filter yields the desired spectral information embedded in the signal, which in our case represents the phase steps. The proposed method offers the advantage of extracting the interference phase of nonsinusoidal waveforms in the presence of miscalibration error of the piezoelectric transducer. In addition, in contrast to previously reported methods, this method does not require the application of selective phase steps between data frames for nonsinusoidal waveforms.     

Phase noise characteristics of narrow-linewidth fiber laser and laser diode in unbalanced interferometers

The phase noises of two narrow-linewidth fiber laser and laser diode are measured by using unbalanced Michelson interferometers with various optical path differences (OPDs). The measured results indicate that the phase noises of the two lasers do not change linearly with the OPD over the range from 1 to 100 m. The laser diode exhibits phase noise levels higher than that of the fiber laser at OPDs longer than 10 m. However, the laser diode outperforms the fiber laser at OPDs shorter than 10 m. The results obtained can assess laser performance and determine the suitable laser for use in a particular application.     

Common-mode noise rejection using fringe-locking method in WEP test by simultaneous dual-species atom interferometers

We theoretically investigate the application of the fringe-locking method(FLM) in the dual-species quantum test of the weak equivalence principle(WEP).With the FLM,the measurement is performed invariably at the midfringe,and the extraction of the phase shift for atom interferometers is linearized.For the simultaneous interferometers,this linearization enables a good common-mode rejection of vibration noise,which is usually the main limit for high precision WEP tests of the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.     

Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers

To increase the accuracy of wave-front evaluation, we propose to exploit the natural capability of multiple lateral shearing interferometers to measure simultaneously more than two orthogonal phase derivatives. We also describe a method, based on Fourier-transform analysis, that uses this multiple information to reconstruct the wave-front under study.     

Optimal phase sensitivity of atomic Ramsey interferometers with coherent spin states

We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose–Einstein condensate in phase accumulation. For large enough particle number N and small phase shift ?, analytical results of the Ramsey signal and the phase sensitivity are derived for a product coherent state |θ,0?. When collisional dephasing is absent, we confirm that the optimal sensitivity scales as 2/N^3/2 for polar angle of the initial state θ = π/4 or 3π/4. The best-sensitivity phase satisfies different transcendental equations, depending upon the initial state and the observable being measured after the phase accumulation. In the presence of the collisional dephasing, we show that the N^-3/2-scaling rule of the sensitivity maintains with spin operators J^x and J^y measurements. A slightly better sensitivity is attainable for optimal coherent state with θ = π/6 or 5π/6.     

Method of phase extraction between coupled atom interferometers using ellipse-specific fitting

We present a method of analysis involving ellipse-specific fitting of sinusoidally coupled data from two gravimeters in a gradiometer configuration. This method permits rapid extraction of induced gradient phase shifts in the presence of common-mode vibrational phase noise. Gravity gradients can be accurately measured in the presence of large vibrational accelerations.     

NMR phase noise in bitter magnets

We have studied the temporal instability of a high field resistive Bitter magnet through nuclear magnetic resonance (NMR). This instability leads to transverse spin decoherence in repeated and accumulated NMR experiments as is normally performed during signal averaging. We demonstrate this effect via Hahn echo and Carr--Purcell--Meiboom--Gill (CPMG) transverse relaxation experiments in a 23-T resistive magnet. Quantitative analysis was found to be consistent with separate measurements of the magnetic field frequency fluctuation spectrum, as well as with independent NMR experiments performed in a magnetic field with a controlled instability. Finally, the CPMG sequence with short pulse delays is shown to be successful in recovering the intrinsic spin--spin relaxation even in the presence of magnetic field temporal instability.     

Thermodynamic formalism of phase transitions in solid solutions

A thermodynamic theory of ferroelectric and ferroelectric-semiconductor solid solutions is presented with account of the effect of hydrostatic pressure in the cases of sharp as well as diffuse transitions. A number of analytical relations are obtained which allow to estimate the effect of admixture concentration and hydrostatic pressure on dielectric permeability, transition temperature, Curie-Weiss constant, heat capacity, thermal expansion coefficient and other properties of crystals with a ferroelectric subsystem. The theoretical results are compared with the experimental data.     

Resonance,phase front,and polarization-independence constraints of inhomogeneous fabry-perot interferometers

The major objective of this paper is to demonstrate the feasibility of imposing local resonance conditions while simultaneously controlling phase front properties upon transmission through slowly-varying Fabry-Perot type interferometers. The interaction of arbitrarily distorted incident phase fronts with double and triple-screened resonators is formulated, and appropriate design procedures are outlined. Special attention is paid to the significant effects of dielectric loading on the effective frequency band and to the cross polarization problem which arises, unavoidably, in conjunction with two-dimensional phase front distortions. The suggested design procedures are demonstrated via concrete numerical examples which are subsequently analyzed throughout a finite (20%) bandwidth.     

Signal distortion noise in volume phase holograms

Signal distortion noise in volume phase holograms is analysed for the case in which the object beam consists of two plane waves. It is shown that, for a given (on-Bragg) signal diffraction efficiency, the magnitude of the signal distortion noise is inversely proportional to the square of crystal thickness. Furthermore, as a function of the angular position of the reconstruction beam, the signal distortion noise has two peaks: one at the Bragg angle and the other at a deviation ₀ from the Bragg angle, where ₀ is a function of relative angles between the components of the object beam and the reference beam. The on-Bragg peak of the signal distortion noise is experimentally located for volume phase holograms recorded in Fe-doped LiNbO₃. The measured angular position is found to be in accord with the calculated value.