## Cold Atom Motion in Optical Fields

#A-854

Cold Atom Motion in Optical Fields

**Tech Area / Field**

- PHY-OPL/Optics and Lasers/Physics
- PHY-ANU/Atomic and Nuclear Physics/Physics

**Status****3** Approved without Funding

**Registration date****14.02.2002**

**Leading Institute**

Engineering Center, Armenia, Ashtarak-2

**Collaborators**

- Institute for Molecular Science, Japan, Okazaki\nUniversitat Wien / Institut fur Experimentalphysik, Austria, Vienna\nHelsinki Institute of Physics, Finland, Helsinki\nUniversity of Connecticut, USA, CT, Storrs\nUniversité Paul Verlain-Metz / Laboratoire de Physique Moleculaire et des Collisions, France, Metz

**Project summary**

*Project's purpose and the state of the art in the field*.

A proposal is set forth to study the control of cold atomic motion using optical fields. With recent developments in atom optics, atom interferometry, and Bose-Einstein condensation, it has become increasingly important to understand the various mechanisms that one can use to modify coherently the center-of-mass motion of atoms. We will undertake a theoretical study of nonlinear atom-field interactions that are particularly designed to achieve targeted states of atomic motion. Of particular interest to the current study are coherent atom beam splitters, matter gratings having period much less than an optical wavelength, and motional states that can arise in the nonlinear spectroscopy of Bose condensates. These topics are among those at the forefront of current research in atomic, molecular and optical physics, and have important applications in nanolithography.

The past several years have been witness to exciting developments in atomic, molecular and optical physics. Bose condensation of a gas of neutral atoms has been observed [1], optical lattices have been used to trap neutral atoms in crystal-like patterns (for a review, see [2]), atoms trapped in 1-D optical potentials have been accelerated and observed to undergo Bloch oscillations [3], and atom interferometers have been used for precision measurements of rotation rates [4], recoil frequencies [5], and the acceleration of gravity [6]. Quasiperiodic optical lattices have been reported [7]. In many of these areas, one encounters situations where atoms are scattered by optical fields. We propose to study the ways in which one can control atomic motion using optical fields.

Our results can have important applications in atom optics, nanolithography, and the manipulation of Bose condensates. In view of present developments in atom optics technology and nanolitography the possible technical developments from this work may be quite substantial.

*Scope of activities and expected Results. *

Among the topics we plan to investigate are:

– Control of time-dependent nonadiabatic processes by an external field including non-linear or multiple or periodic level crossing as well as avoided crossing models for atomic dynamics in the external field of laser radiation governed by both linear and non-linear equations of motion.

– Effects of initial state preparation. In recent experiments, an atomic beam was directed at right angles to a standing wave optical field, and the diffraction pattern was recorded downstream. The observed pattern was seen to behave in an asymmetric, oscillatory manner. It has been suggested that this behavior results from the quantum interference between coherently prepared excited and ground states before the interaction with the standing wave [9]. We plan to study the effect of initial state preparation on quantum scattering. In particular, we will examine methods for controlling matter wave interference fringes by adjusting the phases for atoms prepared in a coherent superposition of magnetic state sublevels.

– Multicolor field geometry. Multiphoton processes are resonant provided n_{1}d_{1}+n_{2}d_{2}=0 for positive integers n1, n2. In this manner one suppresses lower order harmonics and produces an atom density pattern having overall period l/(n_{1}+n_{2}). With moderate field intensities, it should be possible to produce matter gratings having periods as small as 50 nm [8]. A small period matter grating could be used as an efficient scatterer for soft x-rays. A direct application of this technique would allow one to construct large angle matter wave beam splitters and to produce matter wave gratings having periods of order of 100 nm or less.

– Bragg scattering of atoms. We plan to study scattering when the interaction time with the atoms is larger than the inverse recoil frequency. We replace the conventional Bragg scattering geometry by one in which an atomic beam is incident normally on counter propagating optical fields, differing in frequency by an amount d [10]. When d=nw_{q}, an n^{th} order Bragg resonance conditions satisfied. We propose to analyze the field dynamics as atoms are scattering by the counter propagating fields The gain characteristics are expected to be somewhat unusual. It is possible that Bragg lasers can be constructed using this effect, where the active medium is either a well-collimated atomic beam or a Bose condensate.

– Nonlinear spectroscopy of Bose condensates. We plan to look at nonlinear spectroscopy of condensates to see if they lead to new physics or can serve as effective diagnostic probes [11]. We plan to concentrate our efforts on transient spectroscopy. The first case to be considered is "grating echoes". Two, nearly copropagating fields will be pulsed on a condensate to create a spatial modulation. The time evolution of this spatial modulation will be probed by a traveling wave field, applied at different times following the first pulse. The degradation of the grating as a function of time will provide information on the underlying dynamics of the condensate. We also plan to see how a pulsed standing wave field modifies the condensate.

The project consists of 6 blocks of tasks including more than 18 particular issues that include the research work and the dissemination of the results. All the tasks are closely related and are to be performed parallely, during whole the time of the project performance.

Since the work is original then all the work will be presented at International conferences and written up and published in the open scientific literature. With the present paper production rate of the groups it is likely that the final outcome of the project will be at least 18 research publications in the leading refereed journals (Science, Phys. Rev. Lett., Phys. Rev. A, J. Phys. A, etc.).

*Meeting ISTC objectives*.

In accordance with the purposes of ISTC, the proposed Project will assist to form a new research team from scientists and engineers, working in the Engineering Center, who were previously engaged in different defense programs of USSR. This is another dimension of the proposed collaboration, i.e., aside to the pure scientific factors, it is to assist the Armenian group in making transition from weapons-related technology research to non-weapon based research. Due to the strife that followed the break-up of the Soviet Union, Armenia was for quite a while also virtually cut off from mainstream physics. The influx of new thinking that comes with collaboration will undoubtedly steer the Armenian side in the allocation of resources, and guide inpidual scientists so that they can again focus their effort on topics that will make a maximal impact. This is further endorsed by appreciating the ages of the junior members involved in Armenian group. The project will promote for constant increasing of the professional level and for the intimacy of the scientists, complete integration of the members of the group into the international scientific community.

*Competence of the project team. *

The group of Dr. A. Ishkhanyan has a strong background in the field of theoretical atomic and quantum optics. The members of his group are the authors of two important articles on the problem of the coherent multiphoton scattering of neutral atoms by a standing wave optical field. Dr. A. Ishkhanyan is a theorist who proposed a model explanation, based on the quantum interference, of the experimentally observed anomalies in the pattern of coherent diffraction of atoms by short counter propagating pulses of laser radiation [9]. He has much experience in studies of the interactions of an atom with a standing-wave light field, the prototypical optical lattice and, most notably, in the elaborate mathematics that goes into the analytical studies of adiabaticity in quantum systems [12]. As an item that is closely related in methodology, Dr. A. Ishkhanyan and the US collaborators have recently introduced and solved both analytically and numerically a nonlinear generalization of the Landau-Zener model that governs adiabaticity in photoassociation of an atomic Bose-Einstein condensate to a molecular condensate [13].

*Role of foreign collaborators.*

The proposed collaboration is anticipated to be beneficial for all participating partners since it combines extremely high level of expertise for the problems at hand.

Professor Berman has been involved in theoretical research related to the interaction of radiation with matter for over 30 years. Most recently he has worked on problems related to atom interferometry and Bose-Einstein condensation [8,10,14]. As such, the proposed research topic is central to his current research interests. A collaboration with the Armenian group would enable him to expand his research program and to investigate a much wider range of problems than would otherwise be possible.

The collaborators from the University of Connecticut have been involved in theoretical and experimental research related to the interaction of radiation with matter for many years.

The thesis of Prof. Gould was entitled "Momentum Transfer to Atoms by Absorption and Emission of Radiation". Part of this thesis involved the first experiments on the diffraction of atoms, work which is very closely related to that proposed here [15]. His further work concerns to laser cooling and trapping of atoms.

Prof. Javanainen has a long track record in quantum optics style investigations of a Bose-Einstein condensate. This includes the first prediction of the Josephson effect in a double-well trap for a dilute condensate, the first prediction of interference fringes when two condensates overlap, and discussions of adiabaticity a Bose-condensate upon variation of the well depth both in a double-well and in a lattice [16].

Professor Suominen from the Helsinki Institute of Physics leads a well-known research group actively working on several topics of contemporary atomic, molecular and optical physics: interactions between laser-cooled and trapped atoms, Bose-Einstein condensation, creation and time evolution of molecular wave packets, time-dependent quantum systems, quantum information, etc. (see, e.g., [12,13,17]).

Professor Hiroki Nakamura, the Japan collaborator, has been working intensively on the semiclassical theories of both time-dependent and time-independent nonadiabatic transitions (see, e.g., [18]). He has recently obtained the complete solutions of the Landau-Zener-Stueckelberg problems. Also he has proposed a new idea of controlling atomic and molecular dynamic processes by an external filed.

Evidently, the contemplated project represents an ideal mix of the modelling and analytic expertise of the collaborators and the mathematical qualifications of the Armenian team. Undoubtedly, the Armenian group will benefit from contacts with western collaborators. We have worked with these groups before and have several joint publications and thus we have confidence in our ability to be able to cooperate successfully on this project.

The collaborators to this project will participate in the following ways:

— curry out joint research on all the topics of the project,

— conduct regular reviews of progress of work throughout the project effort, review project publications,

— provide technical assistance, conduct joint seminars and workshops.

— help host project personnel visits to the partner countries.

Since the current research interests of the involved groups substantially overlap, it is our clear intention to coordinate closely the work of the four teams by means of information exchange. Communication and intensive collaboration between the groups has been established already. We foresee a promising long-term collaboration in cutting edge science which, we hope, will find deepening continuation in future under internationally funded projects.

*Technical approach and methodology.*

The external field will be considered, as a rule, as a classical one and, if it is necessary, will be quantized. The field is presumed to be quasimonochromatic or consisting of a few number of quasimonochromatic waves with large photon numbers of each mode filling.

As it is well known, the influence of an electromagnetic field on the atoms possesses double character. First, the level populations and the very levels are changed. Second, an exchange of momentum takes place between the field and atom. It is known that these two processes proceed simultaneously and interconnected. Hence, as a rule, atomic inner and translational degrees of freedom are not separated and their behaviour in general is self-consistent. Therefore, the analysis of the problems is also proposed to carry out self-consistently, when the frequency shift and population dynamics, on the one hand, and the atomic centre of mass motion, on the other hand, are equally important.

All the tasks of the project are very complicated and will require a combination of analytical and numerical methods for their solution. However, the main attention will be focused on the analytical methods. Such approach is stimulated by desire to make clear, in first turn, the qualitative aspects of the occurring processes.

The theoretical and mathematical methods for the solution of the most of the formulated tasks are based on the original approaches developed by us for the previous investigations of these and relative problems. In particular, the tasks 1.1 and 3.1 are to be attacked using the approaches developed jointly with the Finland collaborator, Prof. Suominen [12,13] as well as the theory of the Japan collaborator, Prof. Nakamura [18], for searching analytic solutions to the two- and N-state quantum problems. Similarly, the task 1.2 and the most complicated one, task 3.2, is to be treated on the basis of basic results recently derived by the authors in close collaboration with US colleagues [13].

*References.*

1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman and E. A. Cornell, “Obesrvation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269, 198 (1997).

2. P. S. Jessen and I. H. Deutsch, “Optical lattices,” in Advances in Atomic, Molecular and Optical Physics, edited by B. Bederson and H. Walther (Academic Press, San Diego, 1996) pp.95-138.

3. M. Ben-Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).

4. A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation Sensing with an Atom Interferometer” Phys. Rev. Lett. 78, 760 (1997).

5. D. S. Weiss, B. C. Young, S. Chu, “Precision measurement of the photon recoil of an atom using atomic interferometry,” Phys. Rev. Lett. 70, 2706 (1993).

6. M. Kasevich, S. Chu, “Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer,” Appl. Phys. B 54, 321 (1992).

7. L. Guidoni, C. Triche, P. Verkerk and G. Grynberg, Phys. Rev. Lett. 79, 3363 (1997).

8. P. R. Berman, B. Dubetsky, and P. R. Berman, “High resolution amplitude and phase gratings in atom optics,” Phys. Rev. A 58, 4801 (1998).

9. A. M. Ishkhanyan, "Anomalous diffraction of atoms in the field of a standing wave", Laser Physics 7, 1225 (1997); A.M. Ishkhanyan, "Narrowing of interference fringes in diffraction of prepared atoms by standing waves", Phys. Rev. A 61, 063609 (2000); A.M. Ishkhanyan, "Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes", Phys. Rev. A 61, 063611 (2000).

10. P. R. Berman and B. Bian, “Pump-probe spectroscopy approach to Bragg scattering,” Phys. Rev. A 55, 4382 (1997).

11. J. Stenger, S. Innouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569 (1999).

12. A.M. Ishkhanyan, "New analytically integrable models of the two-state problem", Opt. Commun. 176, 155 (2000); A.M. Ishkhanyan, "New classes of analytic solutions of the two-level problem", J. Phys. A: Math. Gen. 33, 5539 (2000); A.M. Ishkhanyan, "New classes of analytic solutions of the three-state problem", J. Phys. A: Math. Gen. 33, 5041 (2000); A.M. Ishkhanyan and K.-A. Suominen, "Solutions of the two-level problem in terms of biconfluent Heun functions", J. Phys. A: Math. Gen. 34, 6301 (2001); A.M. Ishkhanyan and K.-A. Suominen, "Analytic treatment of the polariton problem for a smooth interface", J. Phys. A: Math. Gen. 34, L591 (2001).

13. A. Ishkhanyan, M. Mackie, A. Carmichael, Ph. Gould, and J. Javanainen, “Landau-Zener Problem in Nonlinear Quantum Mechanics”, Phys. Rev. Lett. (2001) (submitted); A.M. Ishkhanyan and K.-A. Suominen, "Analytic model of a three-level system driven by delayed pulses of finite duration ", Phys. Rev. A (2001) (in press).

14. C. P. Search and P. R. Berman, ”Transferring the atom statistics of a Bose-Einstein condensate to an optical field”, Phys. Rev. A 64, 043602 (2001); C. P. Search and P. R. Berman, ”Manipulating the speed of sound in a two-component Bose-Einstein condensate”, Phys. Rev. A 63, 043612 (2001).

15. P.E. Moskowits, P.L. Gould, S.R. Atles, D.E. Pritchard, “Diffraction of an atomic beam by standing-wave radiation”, Phys. Rev. Lett. 51, 370 (1983).

16. J. Javanainen, Phys. Rev. Lett. 57, 3164 (1986); J. Javanainen and S.M. Yoo, Phys. Rev. Lett. 76, 161 (1996); J. Javanainen and M. Yu. Ivanov, Phys. Rev. A 60, 2351 (1999); J. Javanainen, Phys. Rev. A 60, 4902 (1999).

17. J. Piilo, K.-A. Suominen, and K. Berg-Sшrensen,”Cold collisions between atoms in optical lattices”, J. Phys. B: At. Mol. Opt. Phys. 34, L231 (2001); J.-P. Martikainen, K.-A. Suominen, L. Santos, T. Schulte, and A. Sanpera, “Generation and evolution of vortex-antivortex pairs in Bose-Einstein condensates”, Phys. Rev. A 64, 063602 (2001); J. Calsamiglia, M. Mackie, and K.-A. Suominen, “Superposition of macroscopic numbers of atoms and molecules”, Phys. Rev. Lett. 87, 160403 (2001).

18. Hiroki Nakamura, "Nonadiabatic Transition: Concepts, Basic Theories, and Applications" (World Scientific, Singapore, 2002); Yoshiaki Teranishi and Hiroki Nakamura, “Control of Time-Dependent Nonadiabatic Processes by an External Filed”, Phys. Rev. Lett. 81, 2032 (1998).

**The International Science and Technology Center (ISTC)** is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.

ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

### Annual Reports

### Annual Reports

The electronic version of the 2019 Annual Report

2019 Audited Financial Report

view

### Promotional Material

### Значимы проект

See ISTC's new Promotional video
view