arXiv subjects

B. Dubetsky

Publications and source records attributed to B. Dubetsky.

At least 19 recordsLinked to original sources

arXiv2025

Wigner representation enables the exact derivation of the atom interferometer phase, unlike the path integral approach

An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression takes into account precisely gravitational, Coriolis, centrifugal, and gravity-gradient forces, which arise during the rotation of the gravity source at a permanent rate. To achieve this result, we utilized the equations for the atomic density matrix in the Wigner representation. Starting from the exact formula, we derived three new terms in the well-known limit of small rotation angles and short interrogation time, which are attributed to the rotation and translational motion of the platform.

physics.atom-ph↗

arXiv2023

Sequantial large momentum transfer exploiting rectangular Raman pulses

It is proposed to use rectangular Raman pulses for the technique of sequantial large momentum transfer. It is shown that the small parameters that make it possible to use this technology for precision atom interferometry can be 40--200 times smaller than in the case of the Bragg regime. It is predicted that in the case of a non-equidistant timing of auxiliary pulses, one can observe oscillations in time of the interference picture with a period inversely proportional to the recoil frequency. Such an observation would be the first confirmation that Mach-Zehnder atom interference is a phenomenon caused by the quantization of the atomic center-of-mass motion. This effect is calculated for any shape of pulses. One can observe it in the Bragg regime as well. It is proposed to use non-continuous composite Raman pulses as auxiliary beam splitters so that the effective Rabi frequency remains unchanged for the entire process. The gravity phase of an atomic interferometer is calculated for any shape, duration, and timing of Raman pulses, including the Bragg regime. The phase corrections caused by the finite pulses' durations are also calculated for rectangular Raman pulses shape.

physics.atom-ph↗

arXiv2022

Local positioning system as a classic alternative to atomic navigation

A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and orientation of the platform in the frame of the rotating Earth, without solving navigation equations. If there are also velocimeters installed on the platform, then one can restore the velocity and angular rate of the platform rotation in respect to the Earth. Instead of navigational equations, it is necessary to obtain the classical trajectory of a particle in the field of a rotating gravity source. Taking into account the gravity-gradient, Coriolis, and centrifugal forces, the exact expression for this trajectory is derived, which can be widely used in atomic interferometry. A new iterative method for restoring the orientation of the platform without using gyroscopes is proposed. The simulation allowed us to determine the conditions under which the LPS-navigation error per hour is about 10m.

physics.atom-ph↗

arXiv2021

Comment on New apparatus design for high-precision measurement of G with atom interferometry

It is shown that even in the case of a negligibly small change in the gradient of the gravitational field of the mass source in the axial direction, the dependence of this gradient in the radial direction leads to a systematic error in Newton gravitational constant value. The magnitude of this error is calculated for two configurations of the field. For both configurations it was found that this error is larger than the inaccuracy predicted in the article by M. Jain et al [Eur. Phys. J. D 75, 197 (2021)]. In addition, we found the geometry of the source mass, for which this systematic error disappears.

physics.atom-ph↗

arXiv2021

Newtonian gravitational constant measurement. All atomic variables become extreme when using a source mass consisting of 3 or more parts

Atomic interferometry methods used to measure the Newtonian gravitational constant. To improve the accuracy, one should measure the phase of an atomic interferometer at extreme values of atomic vertical velocities and coordinates. Owing to symmetry, the horizontal components of atomic velocities and coordinates are also extreme. We propose using a source mass consisting of 3 or more parts, since only in this case one can find such an arrangement of parts that all atomic variables become extreme. Nonlinear dependences of the phase on the uncertainties of atomic positions and velocities near those extreme values required us to modify the expression for the phase relative standard deviation (RSD). Moreover, taking into account nonlinear terms in the phase dependence on the atomic coordinates and velocities leads to a phase shift. In the last experiment to measure the Newtonian gravitational constant by atomic interferometry, this shift was not included. We took the shift into account, got a value of 199ppm for it, and this leads to a decrease in the value of the Newton constant by 0.02%. In addition, we showed that at equal sizes of the atomic cloud in the vertical and horizontal directions, as well as at equal atomic vertical and transverse temperatures, systematic errors due to the finite size and temperature of the cloud disappear. The calculation also showed that when using the 13-ton source mass proposed recently, the measurement accuracy can reach 17ppm for a source mass consisting of 4 quarters. We assumed that the source mass consisting of a set of cylinders is used for measurements. We have obtained a new analytical expression for the gravitational field of a homogeneous cylinder.

physics.atom-ph↗

arXiv2020

Optimization of the atom interferometer phase produced by the set of cylindrical source masses to measure the Newtonian gravity constant

An analytical expression for the gravitational field of a homogeneous cylinder is derived. The phase of the atom interferometer produced by the gravity field of the set of cylinders has been calculated. The optimal values of the initial positions and velocities of atomic clouds were obtained. It is shown that at equal sizes of the atomic cloud in the vertical and transverse directions, as well as at equal atomic vertical and transverse temperatures, systematic errors due to the finite size and temperature of the cloud disappear. To overcome the influence of the Earth gravitational field on the accuracy of the phase double difference measurement, it is proposed to use the technique of eliminating gravity-gradient terms. After eliminating, one can use extreme values of the atomic positions and velocities. Nonlinear dependences of the phase on the uncertainties of atomic positions and velocities near those extreme values required us to modify the expression for the standard phase deviation. Moreover, such dependences lead to a phase shift, which was also calculated. The relative accuracy of measurements of Newtonian gravitational constant 10^-4 and 2*10^-5 is predicted for sets of 24 and 630 cylinders, respectively.

physics.atom-ph↗

arXiv2019

Asymmetric Mach-Zehnder atom interferometers

It is shown that using beam splitters with non-equal wave vectors results in a new recoil diagram which is qualitatively different from the well-known diagram associated with the Mach-Zehnder atom interferometer. We predict a new asymmetric Mach-Zehnder atom interferometer (AMZAI) and study it when one uses a Raman beam splitter. The main feature is that the phase of AMZAI contains a quantum part proportional to the recoil frequency. A response sensitive only to the quantum phase was found. A new technique to measure the recoil frequency and fine structure constant is proposed and studied outside of the Raman-Nath approximation.

physics.atom-ph↗

arXiv2019

Full elimination of the gravity-gradient terms in atom interferometry

The A. Roura technique was modified to eliminate all terms in the atom interferometer phase, which are linear in the gravity-gradient tensor. The full elimination occurs if all effective wave vectors are slightly changed. The full elimination technique would allow to relieve the synchronization requirements in the test of the Einstein equivalence principle. This technique also eliminates the error of the absolute gravity measurement associated with the gravity gradient terms. The error becomes three orders smaller and does not depend on the time delay between the Raman pulses. In addition, the new differential scheme is proposed to observe the gravity-gradient term independent on the atoms initial position and velocity.

physics.atom-ph↗

arXiv2019

Mach-Zehnder atom interferometer. Quantum and Doppler corrections caused by the finite pulses' durations

A new approach to the theory of atoms' interaction with chirped Raman pulses is developed. When the pulses have sufficiently close effective wave lengths, which are smaller than the atomic cloud size, equations for the family of the matrix elements of the atomic density matrix in the Wigner representation are derived. The solution, involving linear (in the pulse duration) phase corrections, is obtained for the rectangular pulse. The interferometric part of the atoms' excitation is calculated.

physics.atom-ph↗

arXiv2017

Two approaches in the theory of atom interferometry

We compare expressions for the atom interferometer phase obtained using the path integral approach and the approach based on the density matrix equation in the Wigner representation. The power series of these expressions over the Planck constant, truncated to the $\hbar ^{2}$ term, coincide. This coincidence is achieved only after the $Q-$term is included.

physics.atom-ph↗

arXiv2016

Atom interferometry in the presence of an external test mass

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses, and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where the quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.

physics.atom-ph↗

arXiv2015

Atom interferometer phase in the presence of proof mass

This is presented the justification of the expression for the atom interferometer phase in the presence of proof mass used in arXiv:1407.7287. Quantum corrections to that expression are also derived. The corrections allow one to calculate numerically atom interferometer phase with accuracy 1ppm or better.

physics.atom-ph↗

arXiv2014

Optimization and error model for atom interferometry technique to measure Newtonian gravitational constant

Considered contribution to the phase of the atom interferometer caused by the gravity field of the massive proof mass. Demonstrated the method of finding the extrema of this contribution for 100kg Tungsten proof mass of the specific shape and specific parameters of $^{133}Cs$ atom interferometers. Calculated variations of the double difference response under the small deviations of atomic and proof mass variables. The choice of the extremal values of the atomic variables allows one to release requirements for atom positioning on 2 orders of magnitude.

physics.atom-ph↗

arXiv2006

Atom interferometer as a selective sensor of rotation or gravity

In the presence of Earth gravity and gravity-gradient forces, centrifugal and Coriolis forces caused by the Earth rotation, the phase of the time-domain atom interferometers is calculated with accuracy up to the terms proportional to the fourth degree of the time separation between pulses. We considered double-loop atom interferometers and found appropriate condition to eliminate their sensitivity to acceleration to get atomic gyroscope, or to eliminate the sensitivity to rotation to increase accuracy of the atomic gravimeter. Consequent use of these interferometers allows one to measure all components of the acceleration and rotation frequency projection on the plane perpendicular to gravity acceleration. Atom interference on the Raman transition driving by noncounterpropagating optical fields is proposed to exclude stimulated echo processes which can affect the accuracy of the atomic gyroscopes. Using noncounterpropagating optical fields allows one to get a new type of the Ramsey fringes arising in the unidirectional Raman pulses and therefore centered at the two-quantum line center. Density matrix in the Wigner representation is used to perform calculations. It is shown that in the time between pulses, in the noninertial frame, for atoms with fully quantized spatial degrees of freedom, this density matrix obeys classical Liouville equations.

physics.atom-ph↗

arXiv2002

$\fracλ{8}$-period optical potentials

A Raman configuration of counterpropagating traveling wave fields, one of which is $lin\bot lin$ polarized and the other $lin\Vert lin$ polarized, is shown to lead to optical potentials having $\fracλ{8}$ periodicity. Such optical potentials may be used to construct optical lattices having $% \fracλ{8}$ periodicity. Using numerical diagonalization, we obtain the optical potentials for $^{\text{85}}$Rb atoms.

physics.atom-ph↗

arXiv2002

Nanometer scale period sinusoidal atom gratings produced by a Stern-Gerlach beam splitter

An atom interferometer based on a Stern-Gerlach beam splitter is proposed. Atom scattering from a combination of magnetic quadrupole and homogeneous magnetic fields is considered. Using Raman transitions, atoms are coherently excited into and de-excited from sublevels having nonzero magnetic quantum numbers. The spatial regions in which the atoms are in such sublevels are small and have magnetic fields designed to have constant gradients. Therefore, the atoms experience position-independent accelerations, and the aberration of the coherently separated and recombined atomic beams remains small. We find that because of these properties it is possible to envision an apparatus producing atomic density gratings with nm-scale periods and large contrasts over 10-100 $μ$m. We use a new method of describing the atomic interaction with a pulsed spatially homogeneous field. In our detailed analysis, we calculate corrections caused by the non-linear part of the potential and the finite value of the de-Broglie wave length. The chromatic aberration and the effects of an angular beam divergence are analyzed, and optimal conditions for an experimental demonstration of the technique are identified.%The $lin\bot %lin$ combination of resonant co-propagating traveling waves splits %atoms between different Zeeman sublevels. %For a given desirable atom %grating period and length, characteristics of the atomic beam and %magnetic field are found from requirements that corrections remain %below $10%.$

physics.atom-ph↗

arXiv2002

$λ/4$, $λ/8$, and higher order atom gratings via Raman transitions

A method is proposed for producing atom gratings having period $λ/4$ and $λ/8$ using optical fields having wavelength $λ$. Counterpropagating optical fields drive Raman transitions between ground state sublevels. The Raman fields can be described by an effective two photon field having wave vector 2 k, where k is the propagation vector of one of the fields. By combining this Raman field with {\em another} Raman field having propagation vector -2 k, one, in effect, creates a standing wave Raman field \label{91}%which whose ``intensity'' varies as $\cos (4 k\cdot r).$ When atoms move through this standing wave field, atom gratings having period $λ/4$ are produced, with the added possibility that the total ground state population in a given ground state manifold can have $λ/8$ periodicity. The conditions required to produce such gratings are derived. Moreover, it is shown that even higher order gratings having periodicity smaller than $λ/8$ can be produced using a multicolor field geometry involving three (two-photon) Raman fields. Although most calculations are carried out in the Raman-Nath approximation, the use of Raman fields to create reduced period optical lattices is also discussed.

physics.atom-ph↗

arXiv2001

Atom gratings produced by large angle atom beam splitters

An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile arising after scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. It is shown that, owing to the scattering in these potentials, two \QTR{em}{groups} of momentum states are produced rather than two distinct momentum components. The corresponding spatial density profile is calculated and found to differ significantly from a pure sinusoid.

physics.atom-ph↗