## Schrodinger Cat States of Light

#A-1898

Experimental Realization of (Schrödinger Cat-Like) Linear Superposition of Two Coherent States of Optical Field

**Tech Area / Field**

- PHY-OPL/Optics and Lasers/Physics

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

**Registration date****28.09.2010**

**Leading Institute**

Institute for Physical Research, Armenia, Ashtarak-2

**Collaborators**

- University of Arkansas / Fulbright College of Arts and Sciences, USA, AR, Fayetteville

**Project summary**

*The Project aim.*The basic aim of the Project is experimental obtaining of two-component Schrödinger cat-like superposition states of light. Within the Project theoretical studies of possibility to obtain multicomponent superposition states of optical field will also be performed.

*Current status.* Obtaining and detection of macroscopic quantum-mechanical superposition states (like Schrödinger cat states [1]) is of great interest in contemporary quantum optics [2]. Cat states and other coherent-state superpositions have been proposed to implement various quantum information tasks such as linear-optics quantum computation [3,4] and quantum metrology [5-7]. Experimental observation of these states was recently realized in works [8] (with laser-cooled ions) and [9] (with Rydberg states of atoms). The possibility of obtaining such states has for the first time been shown in work [10] for propagation of single-mode radiation in a medium with Kerr nonlinearity. In works [11-13] it was shown that single-photon absorption leads to decay of the superposition state into incoherent (statistical) mixture of its components. In this case, as shown in [14-17], destruction of coherence occurs, in general, much faster than the dissipation of energy. Work [18] shows the possibility of formation of even type of superposition states of light in the process of generation of the second sub-harmonic, in the range of small values of the photon number. Works [19-22] also investigate superposition states. In work [23] the density matrix equations have been solved numerically and it was shown that the two-component quantum superposition states (superposition of two opposite-phase coherent states) may be obtained as a result of two-photon absorption processes at parametric quadratic perturbation (whose operator may be represented via squares of field operators) of a nonlinear medium. These states are even or odd (depending on the initial conditions). It was shown that even small one-photon absorption destroys the superposition state. We considered the same problem [24] by simulating quantum trajectories of the system [25]. We showed that in the presence of weak one-photon absorption it is possible that at long evolution time and for small values of the state amplitude an even-type superposition state be formed in the system. This is associated with the fact that in the range of small state-amplitudes the system spends, on quantum trajectories, much longer time in the even superposition state than in odd one. We studied then in [26, 27] the possibility to obtain a three-component superposition state (superposition of three coherent states differing in phase by 2/3). Here the process of three-photon absorption has been considered in case of externally three-photon-parametrically excited absorbed mode. We have shown that such states are eigenstates of the cube of the photon annihilation operator and that there are three types of these states, which differ from each other by type of interference between the coherent components (recall that the two-component superposition states are eigenstates of the square of annihilation operator and there are two types of these states, even and odd, which differ by the type of interference between the coherent components). In the above-cited work [26] we studied the influence of one-, two-, and three-photon dissipation on the three-component superposition states. It was shown that one- and two-photon dissipation destroys the superposition state into incoherent (statistical) mixture of the coherent components. The next work [27] investigates the system by the quantum trajectory technique and shows that in case of presence of weak one-photon absorption and in the range of small values of the amplitude of the state of system the field may be found in the three-component superposition state. This is associated with the fact that in this range of interaction in quantum trajectories the system spends in one type of superposition states much longer time than in two other types.

*The project’ influence on progress in this area.* Implementation of the Project will strongly promote development of not only fundamental science, but also the technology of creation of quantum computers.

*The participants’ expertise.* Scientists of Institute for Physical Research (IPR) have traditionally high level of studies in laser physics and optics. Theoretical justification of experimental investigations proposed in the Project is developed in the works of Project Manager S. T. Gevorgyan and V. O. Chaltykyan [24, 26-27]. Competence of participants corresponds to their publications listed in Detailed Project Information.

*Expected results and their application.* We expect to obtain experimentally two-component superposition state of light. As mentioned above, these studies will be applicable to development of quantum computers. We also plan to prepare a model of a device, which is a source of optical field in Schrödinger cat-like superposition state. The device which will be fabricated on the basis of this model may be used in research laboratories and in universities for training students studying quantum optics and quantum mechanics.

*Meeting the ISTC goals and objectives. *Corresponding to the ISTC goals, the proposed Project will enable organizing a new team of scientists and engineers for conducting scientific studies with peaceful purposes. In the framework of the Project the collaboration will be continued between the research groups of USA (University of Arkansas) and Armenia (IPR); this will promote the integration of Armenian team members into international scientific community. Experimental arrangements developed during execution of the Project may be used for solving various scientific and technical problems, as well as serve as a basis for organizing small science intensive industries, promoting thus the development of Armenian economics.

*Scope of activities. *The duration of the Project will be 30 months. The Project consists of two parts, experimental and theoretical.

We propose an experimental study of the two-photon absorption process in case where the absorbed mode is externally excited in two-photon parametric way. The distribution of photon numbers in the two-photon absorbed field will be measured. This distribution should have for cat-like state an oscillatory structure at the two-photon frequency.

Measurement of the coefficient of two-photon absorption will be performed via measuring the intensity correlation function at the input and output of nonlinear medium.

The process of two-photon parametric excitation will be simulated and the source of such excitation will be experimentally obtained.

For the parameters of nonlinear medium and excitation the equation for the density matrix of the field will be solved numerically and then the dynamics of the quantum entropy will be calculated by means of density matrix. This dynamics will make possible to determine the time domain when the cat state of optical field was formed in the system.

*Role of Foreign Collaborators/Partners.* Groups of IPR and University of Arkansas had collaborated and have joint publications; therefore we are aware of successful collaboration in the present Project. Exchanges of information and scientific ideas with the foreign collaborators are due during the whole project, as well as joint solving of scientific problems and publication of articles is expected. Collaborator will coordinate the experimental works to be performed and monitor the quarter reports.

*Technical approach and methodology.* In the experiment the distribution of photon numbers in the mode which is absorbed in the medium in two-photon way will be recorded. The absorbed mode will be excited externally by two-photon parametric process. If a cat-like state will be produced, the function of distribution of numbers of photons will oscillate at the two-photon frequency. We also intend to obtain theoretically the density matrix and the Wigner function of multicomponent cat-like superposition states.

REFERENCES

- E. Schrцdinger, Naturwissenschaften, 23, 807 and 823 (1935).
- V. Buzek, and P. L. Knight, Progres in Optics, edited by E. Wolf (North Holland: Amsterdam) (1995).
- T. C. Ralph, A. Gilcrist, G. J. Milburn, W. J. Munro, and S. Glancy, Phys. Rev. A, V. 68, 042319 (2003).
- A. P. Lund, T. C. Ralph, and H. L. Haselgrove, Pys. Rev. Lett., V. 100, 030503 (2008)
- T. C. Ralph, Phys. Rev. A, V. 65, 042313 (2002).
- W. J. Munro, K. Nemoto, G. J. Milbum, and S. L. Braunstein, Phys. Rev. A, V. 66, 023819 (2002).
- A. Gilchrist et al., J. Opt. B: Quantum Semiclassical Opt. 6, S828 (2004).
- C. Monroe, D. M. Meekhot, B. E. King, D. V. Wineland, Science, V. 272, p. 1131 (1996).
- M. W. Noel, C. R. Stroud, Phys. Rev. Lett., V 77, p. 1913 (1996).
- B. Yurke, and D. F. Stoler, Phys. Rev. Lett., V. 57, p. 13 (1986).
- Ts. Ganstog, R. Tanas, Phys. Rev A, V. 44, p.2086 (1991).
- W. Schleich, M. Pernigo, L. F. Kien, V. 44, p.2172 (1991).
- V. Buzek, A. Vidiella-Barranco, P. L. Knight, Phys. Rev. A, V. 45, p.6570 (1992).
- W. H. Zurek, Phys. Today, V. 44, p.36 (1991).
- W. H. Zurek, S. Habib, J. P. Paz, Phys. Rev. Lett, V. 70, p.1187 (1993).
- E. Joos, H. D. Zeh, Z. Phys. B, V.59, p.223 (1985).
- D. F. Walls, and G. J. Milburg, Phys. Rev A, V. 31, p.2403 (1985).
- M. Wolinsky, H. J. Carmichael, Phys. Rev. Lett., V. 60, p.1836 (1988).
- J. Dea-Banacloce, Phys. Rev. Lett., V. 65, p. 3385 (1990).
- V. Buzek, H. Moya-Cessa, P. L. Knight, S. J. D. Phoenix, Phys. Rev. A, V. 45, p. 8190 (1992).
- Anne E. B. Nielsen, Uffe V. Poulsen, Antnio Negretti, and Klaus Molmer, Phys. Rev. A, V. 79, 023841 (2009).
- Bing He, Mustansar Nadeem, and Janos A. Bergou, Phys. Rev. A, V. 79, 035802 (2009).
- L. Gilles, B. M. Garraway, P. L. Knight, Phys. Rev A, V. 49, p. 2785 (1994).
- S. T. Gevorgyan and V. O. Chaltykyan, J. of Modern Optics, V. 51, no 13, p. 1911 (2004).
- K. Molmer, Y. Gastin, J. Dalibard, JOSA B, V 10, p. 524 (1992).
- S. T. Gevorkyan and V. O. Chaltykyan, J. of Modern Optics, V. 46, no. 10, p. 1447 (1999).
- S. T. Gevorgyan, Min Xiao, V. O. Chaltykyan, J. of Modern Optics, V. 55, no. 12, p. 1923 (2008).

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