^{1,a)}

### Abstract

A new quantum control scheme for general multilevel systems using intense laser fields is proposed. In the present scheme, the target subspace consisting of several quantum levels is effectively isolated by applying intense cw lasers with specific conditions. The formulation is carried out using the Green function with the help of projection operator method. Dynamics of the isolated target subspace is governed by an effective Hamiltonian. The developed scheme is applied to the quantum control of dissipative four- and five-level systems. It is clarified that the present method makes it possible not only to manipulate the coherent population dynamics but also to suppress the dissipative dynamics.

This research was supported, in part, by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research(C), KAKENHI (Grant No. 20550021).

I. INTRODUCTION

II. THEORETICAL

III. APPLICATIONS

A. Branch-type four level system

B. Five-level system

IV. SUMMARY

### Key Topics

- Population dynamics
- 15.0
- Eigenvalues
- 10.0
- Subspaces
- 6.0
- Green's function methods
- 5.0
- Control theory
- 4.0

## Figures

Schematic of space separation for a general multilevel quantum system.

Schematic of space separation for a general multilevel quantum system.

Schematic of the branch-type four-level system.

Schematic of the branch-type four-level system.

Population dynamics of the branch-type four-level system with under the laser conditions; (a) , , (b) , , (c) , , and (d) , . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Population dynamics of the branch-type four-level system with under the laser conditions; (a) , , (b) , , (c) , , and (d) , . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Population dynamics of the branch-type four-level system with under the laser conditions; (a) , , (b) , , (c) , , and (d) , . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Population dynamics of the branch-type four-level system with under the laser condition , with various as follows; (a) , (b) , (c) , and (d) . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Population dynamics of the branch-type four-level system with under the laser condition , with various as follows; (a) , (b) , (c) , and (d) . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Population dynamics of the branch-type four-level system with under the laser condition , with various as follows; (a) , (b) , (c) , and (d) . Thin solid and thin broken lines denote the exact population dynamics of and , respectively. Thick solid and thick broken lines denotes the population dynamics of and calculated by the effective Hamiltonian, respectively. The area with light gray denotes the population which escapes to the -space.

Schematic of the branch-type five-level system.

Schematic of the branch-type five-level system.

Population dynamics of the branch-type five-level system with under the laser conditions; (a) , , (b) , , (c) , , and (d) , . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated by effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

Population dynamics of the branch-type five-level system with under the laser conditions; (a) , , (b) , , (c) , , and (d) , . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated by effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

Population dynamics of the five-level system with under the laser condition , with various as follows; (a) , (b) , and (c) . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated with effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

Population dynamics of the five-level system with under the laser condition , with various as follows; (a) , (b) , and (c) . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated with effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

(a) Time dependence of the laser pulse envelope function with the parameters, , , , and . Dark gray solid line, light gray broken line and dark broken line denote pulse envelope functions which correspond to , and , respectively. (b) Population dynamics of the five-level system with and under the laser condition , . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated with effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

(a) Time dependence of the laser pulse envelope function with the parameters, , , , and . Dark gray solid line, light gray broken line and dark broken line denote pulse envelope functions which correspond to , and , respectively. (b) Population dynamics of the five-level system with and under the laser condition , . Thin solid, broken, and dotted lines denote the exact population dynamics of , , and . Thick dark gray solid, thick light gray broken, and thick dark broken lines denote the population dynamics of , , and calculated with effective Hamiltonian, respectively. The area filled with light gray denotes the sum of the -space population and the lost population.

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