Identification and reduction of effective dimensions of quantum systems

Abstract

Abstract:

Considering dynamics of a pulse-driven finite-dimensional quantum system with near degenerate eigenstates, the multi-level system includes one ground state and a number of excited states, in which the transitions exist between the ground state and any excited state. Population transfer induced by different kinds of pulses in this multi-level system were investigated. It is noted that in the case of both weak and strong fields, the quantum system can be reduced to a two-level system. Analytical relations between the original system and the reduced system are obtained for weak fields with multi frequencies and strong fields with one frequency. These results could be generalized to a multi-level system with several sets of near-degenerated eigenstates, and the conclusion could be utilized to identify the effective dimension of a quantum multi-level system controlled by laser.

Key words: quantum control, population transfer, laser pulses, dimension reduction

CLC Number:

O431.2

XU Qiang, SHUANG Feng. Identification and reduction of effective dimensions of quantum systems[J]. J4, 2012, 29(3): 316-322.

References

[1] Chu S. Cold Atoms and Quantum Control [J]. Nature, 2002, 416(6877): 206-210.
[2] Peirce A P, Dahleh M A, Rabitz H. Optimal-control of quantum-mechanical systems - existence, numerical approximation, and applications [J]. Physical Review A, 1988, 37(12): 4950-4964.
[3] Assion A, Baumert T, Bergt M, Brixner T, Kiefer B, Seyfried V, Strehle M, Gerber G. Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses [J]. Science, 1998, 282: 919.
[4] YANG Jie, CONG Shuang. Research on models of open quantum system interacted with bath [J]. Chinese Journal of Quantum Electronics (量子电子学报)，2011, 28(6): 660-673 (in Chinese).
[5] CONG Shuang, LOU Yue-sheng. Decoherence and control strategies in open quantum systems [J]. Chinese Journal of Quantum Electronics (量子电子学报)，2008, 25(6): 665-669 (in Chinese). [6] Gaubatz U, Rudecki P, Schiemann S, Bergmann K. Population transfer between molecular vibrational levels by stimulated raman scattering with partially overlapping laser fields. a new concept and experimental results [J]. J. Chem. Phys., 1900, 92: 5363.
[7] Kobrak M N, Rice S A. Selective photochemistry via adiabatic passage:An extension of stimulated raman adiabatic passage for degenerate final states [J]. Phys. Rev. A, 1998, 57(2885): 2885.
[8] Schleich W P. Quantum Control: Sculpting a Wavepacket [J]. Nature, 1999, 397(6716): 207-208.
[9] Cook R J, Shore B W. Coherent dynamics of n-level atoms and molecules. iii. an analytically soluble periodic case [J]. Phys. Rev. A, 1979, 20:539.
[10] Shore B W, Cook R J. Coherent dynamics of n-level atoms and molecules.iv. two- and three-level behavior [J]. Phys. Rev. A, 1979, 20:1958.
[11] Eberly J H, editor. Optics Express, Focus Issue: Control of Loss and Decoherence in Quantum Systems, volume 02 of 09, April 1998.
[12] Akramine O El, Makhoute A. The kinetics of the atomic relaxation induced by laser noise [J]. J. Phys. B, 1998, 31:4349.
[13] Bergmann K, Theuer H, Shore B W. Coherent population transfer among quantum states of atoms and molecules [J]. Reviews Of Modern Physics, 1998, 70(3):1003-1025.
[14] Xu R., Yan Y J, Ohtsuki Y, Fujimura Y, Rabitz H. Optimal control of quantum non-markovian dissipation: Reduced liouville-space theory [J]. J. Chem. Phys, 2004, 120:6600.
[15] Shuang Feng, Rabitz H. Cooperating or fighting with control noise in the optimal manipulation of quantum dynamics [J]. J. Chem. Phys., 2004, 121(19):9270–9278.
[16] Shuang Feng, Rabitz H. Cooperating or fighting with decoherence in the optimal control of quantum dynamics [J]. J. Chem. Phys., 2006, 124(15):154105.
[17] Shuang Feng, Rabitz H, Dykman M. Foundations for cooperating with control noise in the manipulation of quantum dynamics [J]. Phys. Rev. E, 2007, 75(2):021103.
[18] Shuang Feng, Zhou Mianlai, Pechen Alexander, Wu Rebing, Shir Ofer, Rabitz H. Control of quantum dynamics by optimized measurements [J]. Phys. Rev. A, 2008, 78(6):063422.
[19] Jean Claude Diels and Wolfgang Rudolph. Ultrashort laser pulse phenomena fundamentals, Techniques,and Applications on a Femtosecond Time Scale. Academic Press, San Diego,1996 [20] Frasca M. Perturbative results on localization for a driven two-level system [J]. Physical Review B, 2003, 68(16): 165315.
[21] Rabi I I, Ramsey N F, Schwinger J. Use of Rotating Coordinates in Magnetic Resonance Problems [J], Rev. Mod. Phys., 1954, 26:167-171
[22] Shore B W. The Theory of Coherent Atomic Excitation, Wiley, 1990.
[23] Xu Qiang, Wang Yaoxiong, Rabitz H, Shuang Feng. Identification of dimensions of quantum systems controlled by lasers. in progress.