Нестандартные оптические проявления квантовой геометрической фазы тема диссертации и автореферата по ВАК РФ 01.04.05, кандидат наук Ростом Айхам

• Ростом Айхам
• кандидат наук
• 2022

Введение диссертации (часть автореферата) на тему «Нестандартные оптические проявления квантовой геометрической фазы»

Abstract

Anholonomy is a purely geometric feature of the physical evolution. During this process, the physical system fails to return to its original state after a cyclic evolution, leading to a rotation by a non-integrable (path-dependent) phase angle called the geometric phase. The quantum theory deals with indistinguishable processes and describes their physical effects through the expectation values and probabilities, which can be derived from the interference between probability amplitudes. In such a quantum structure of interference between complex quantities, the geometric phase factor must be a key element. It carries non-trivial information about the geometry or topology of the quantum evolution and shifts the dynamical oscillations of the quantum interference pattern.

The geometric phase is a kinematic notion that accompanies any kind of evolution of the physical system (classical, quantum, discrete, continuous, adiabatic, non-adiabatic, cyclic, and open). However, it has been studied only for the most general types of quantum states, i.e., for noncompound isolated pure or mixed quantum states.

The present work investigates the role that the geometric phase plays in open and composite quantum systems. This includes an atomic Bose-Einstein condensate localized in the minima of a double-well optical potential with irreversible photon loss, the evolution of subspaces of quantum states, and optical interferometry under system-environment nondestructive interaction.

It has been found that the optical geometric phase can cause a remarkable modification of the state of Bose-Einstein condensate. The amount of modification can be revealed by studying the tunneling between the atomic localizations. Moreover, the geometric phase can be defined not only for the evolution of vectors in the Hilbert space, but also for the evolution of subspaces. It is also shown that the operation on the geometric phase in interferometry is the optimal strategy for postselected quantum metrology.

The results of the dissertation are of particular importance for our fundamental understanding of quantum correlations and for practical applications in quantum metrology and control.

Заключение диссертации по теме «Оптика», Ростом Айхам

Conclusion

The present dissertation is devoted to the study of the nonstandard manifestations of the quantum geometric phase. The main results of the dissertation can be summarized in the following four points:

• A method for detecting an optically-generated geometric phase has been proposed. In a composite quantum system consisting of photons and a two-mode atomic Bose-Einstein condensate, the geometric phase can be generated in the photonic mode by adjusting the parameters of the pumping electromagnetic field, and transferred through the entanglement to the Bose-Einstein condensate. The created geometric phase can be observed by studying its effects on the atomic tunneling between the modes. The proposed method can be regarded also as a technique for controlling the state of the condensate.

• The concept of the pure-state geometric phase is generalized to the subspace of states. We have shown that when the total space is characterized by zero geometric phase, the subspaces may have a nonzero geometric phase. The difficulty in calculating the geometric phase for a particular subspace can be circumvented by finding the geometric phase of the other orthogonal subspace.

• The operational approach of the geometric phase has been extended to open quantum systems undergoing nonunitary evolution. A qubit passing through a sequence of Mach-Zehnder interferometers exhibits a geometric phase at the output that depends on the history of contacts of the qubit with the environment.

• The concept of the geometric phase is generalized to the "two-state vector formalism". It is shown that the operation on the geometric phase is the optimal strategy for amplification and phase estimation issues. A single photon resulting from "out-of-phase" interference in the postselected system can impart a n phase shift to the other photon interacting weakly with it in a nonlinear optical medium. Furthermore, a pair of photons, initially prepared in a product state, can be entangled in a non-maximally entangled

state through an intermediate weak interaction and a subsequent merging of out-of-phase quantum states. The non-maximally entangled state is a strong correlation between rare events that can help in perfectly suppressing the "technical" noise.

Finally, the studying of the geometric phase in open and composite quantum systems can provide novel insights into the quantum world, offer a more comprehensive understanding of it, and show how to improve our current quantum sensors.

Список литературы диссертационного исследования кандидат наук Ростом Айхам, 2022 год

Publications

Articles in peer-reviewed journals:

1. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Geometric phase transferred from photonic mode to atomic BEC. Optics Communications 436, 52 (2019). https://doi.org/10.1016/j.optcom.2018.12.001

2. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Geometric phase for "dark" subspaces in coherent population trapping. Modern Physics Letters B, 2150021 (2020). https://doi.org/10.1142/S0217984921500214

3. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Geometric phase in open quantum system as a function of its history. Quantum Studies: Mathematics and Foundations 6, 217(2019).

https://doi.org/10.1007/s40509-018-00179-x

4. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Quantum geometric phase under pre-and post-selection. Quantum Electronics 49, 439 (2019). https://doi.org/10.1070/QEL17014

5. A. Rostom. Interference in between the acts of pre- and post-selection. Quantum Electronics 50, 595 (2020).

https://doi.org/10.1070/QEL17335

6. A. Rostom. Optimal settings for amplification and estimation of small effects in postselected ensembles. Annalen der Physik 534, 2100434 (2021). https://doi.org/10.1002/andp.202100434

Conferences:

1. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Geometric phase transferred from photonic mode to atomic BEC. Physics of ultra-cold atoms. Novosibirsk, Russia (2018).

2. V. Tomilin, T. Yakovleva, A. Rostom, L. Il'ichov. Geometric phase in non-standard settings. Modern problems of laser physics. Novosibirsk, Russia (2018).

3. T. Yakovleva, A. Rostom, V. Tomilin, L. Il'ichov. Geometric phase as a measurement history function. 20th Anniversary of Superconducting Qubits: progress and future di-

rections. Tsukuba, Japan (2019).

4. A. Rostom. Interference in between the acts of pre- and post-selection. Physics of ultra-cold atoms. Novosibirsk, Russia (2019).

5. A. Rostom. "Detection of weak 'two-photon' cross-Kerr nonlinearity using the 'two-state vector formalism' of quantum mechanics". Physics of ultra-cold atoms. Novosibirsk, Russia (2020).

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