在論文主要在研究電磁引發透明條件下光和物質交互作用的量子性質。此文中使有限數量的原子與兩個電磁波交互作用，第一個是很強的古典場，第二個是可用量子力學描述很弱的探測電磁場。一種臨界的耦合強度會在量子相變發生的時候被揭露。我們提供了它在某些特定狀態的應用，做為介觀數量原子的量子記憶體。我們用數值計算來證明透過古典場的絕熱控制，把量子態轉移到原子系統是可行的，且這個原子系統達到拉曼共振的條件時，會將已儲存的光子以高保真度取回量子場。此外，可證明不必使用無限數量的原子來把光子態儲存到原子系統，只要光子的希爾伯特空間的維度等於或小於原子的數量。為了證明記憶體可用在非平凡態，我們用二相式態做為例子：用在有限大小的光子態類相干的性質。

In this thesis we study the quantum properties of light-matter interaction under the electrically induced transparency configuration. Here, a finite number of atoms interact with two electromagnetic fields one assumed to be a strong field treated classically and the second one, a weak probe, which description is done by means of a quantum mechanics. A critical coupling strength is revealed at which quantum phase transition occurs. The application of this scheme, with a mesoscopic number of atoms, as a quantum memory is also provided for particular states. Numerical calculations are used to proof that by adiabatic control of the classical field it is possible to transfer the quantum state of the field into the atomic system, with the retrieval of this stored photons back to the field with a high fidelity if Raman resonance condition is achieved. Additionally, It is shown that an infinite number of atoms are not required to store a photonic state in the atomic system as long as the Hilbert space of the photons is of equal or smaller dimensions than the number of atoms. In order to justify the use of this memory on non trivial states binomial states are introduced as an example of finite-sized photonic states whit coherent-like properties.

[1] Jones, N. “The quantum company: DWave
is pioneering a novel way of making
quantum computers–but it is also courting controversy.” Nature, 498(7454), 286289.
(2013).
[2] Castelvecchi, D. IBM’s quantum cloud computer goes commercial.” Nature News,
543(7644), 159. (2017).
[3] Benioff, P. “The computer as a physical system: A microscopic quantum mechanical
Hamiltonian model of computers as represented by Turing machines’. Journal
of statistical physics, 22(5), 563591
(1980).
[4] Gross, M., and Haroche, S. “Superradiance: An essay on the theory of collective
spontaneous emission. Physics reports, 93(5), 301396.(
1982).
[5] Shor, P. W. “Algorithms for quantum computation: Discrete logarithms and factoring.”
In Proceedings 35th annual symposium on foundations of computer science
(pp. 124134).
Ieee.(1994).
[6] Wang, J. Y., Yang, B., Liao, S. K., Zhang, L., Shen, Q., Hu, X. F., ... and Zhong,
B. “Direct and fullscale
experimental verifications towards ground–satellite quantum
key distribution.” Nature Photonics, 7(5), 387.(2013)
[7] Ritter, S., Nölleke, C., Hahn, C., Reiserer, A., Neuzner, A., Uphoff, M., ... and
Rempe, G. “An elementary quantum network of single atoms in optical cavities”.
Nature, 484(7393), 195. (2012).
[8] Terraciano, M. L., Knell, R. O., Norris, D. G., Jing, J., Fernández, A., and Orozco,
L. A. “Photon burst detection of single atoms in an optical cavity.” Nature Physics,
5(7), 480. (2009).
[9] Buluta, I., Ashhab, S., and Nori, F. “Natural and artificial atoms for quantum computation.”
Reports on Progress in Physics, 74(10), 104401. (2011).
[10] Stoler, D., Saleh, B. E. A., and Teich, M. C. “Binomial states of the quantized radiation
field. Optica Acta: International Journal of Optics”, 32(3), 345355.
(1985).
[11] VidiellaBarranco,
A., and Roversi, J. A. “Statistical and phase properties of the
binomial states of the electromagnetic field”. Physical Review A, 50(6), 5233.
(1994).
[12] Dattoli, G., Gallardo, J., and Torre, A. “Binomial states of the quantized radiation
field: comment.” JOSA B, 4(2), 185187.
(1987).
[13] Arecchi, F. T., Courtens, E., Gilmore, R., and Thomas, H. “Atomic coherent states
in quantum optics.” Physical Review A, 6(6), 2211. (1972).
[14] Gerry, C., Knight, P., and Knight, P. L. “Introductory quantum optics.” Cambridge
university press. (2005).
[15] Li, K. C., Meng, X. G., and Wang, J. S. “Phase Space Analysis of the Twomode
Binomial State Produced by Quantum Entanglement in a Beamsplitter.” International
Journal of Theoretical Physics, 110.
(2019).
[16] Lambert, N., Emary, C., and Brandes, T. “Entanglement and the phase transition
in singlemode
superradiance.” Physical Review Letters, 92(7), 073602. (2004).
[17] Gilmore, R., Bowden, C. M., and Narducci, L. M. “Classicalquantum
correspondence
for multilevel systems.” Physical Review A, 12(3), 1019. (1975).
[18] Jaynes, E. T., and Cummings, F. W. “ Comparison of quantum and semiclassical
radiation theories with application to the beam maser.” Proceedings of the IEEE,
51(1), 89109.
(1963).
[19] Wang, Y. K., and Hioe, F. T. “ Phase transition in the Dicke model of superradiance”.
Physical Review A, 7(3), 831. (1973).
[20] Rabi, I. I. “On the process of space quantization.” Physical Review, 49(4), 324.
(1936).
[21] R. H. Dicke, “Coherence in Spontaneous Radiation Processes,” Phys. Rev. 93, 99
(1954).
[22] M. Tavis and F. W. Cummings, “Exact Solution for an NMolecule—
RadiationField
Hamiltonian,” Phys. Rev. 170, 170 (1968).
[23] Y. K. Wang and F. T. Hioe, “Phase Transition in the Dicke Model of Superradiance,”
Phys. Rev. A 7, 831 (1973).
[24] M. O. Scully, E. S. Fry, C. H. Raymond Ooi, and K. Wodkiewicz, “Directed Spontaneous
Emission from an Extended Ensemble of N Atoms: Timing Is Everything,”
Phys. Rev. Lett. 96, 010501 (2006).
[25] M. O. Scully and A. Svdzinsky, “The Super of Superradiance,” Science 325, 1510
(2009).
[26] G. Chen, Z. Chen, and J.Q.
Liang, “Groundstate
properties for coupled BoseEinstein
condensates inside a cavity quantum electrodynamics,” Europhys. Lett.
80, 40004 (2007).
[27] Q.H.
Chen, T. Liu, Y.Y.
Zhang, and K.L.
Wang, “Quantum phase transitions in
coupled twolevel
atoms in a singlemode
cavity,” Phys. Rev. A 82, 053841 (2010).
[28] N. Lambert, C. Emary, and T. Brandes, “Entanglement and the Phase Transition
in SingleMode
Superradiance,” Phys. Rev. Lett. 92, 073602 (2004).
[29] J. Vidal and S. Dusuel, “Finitesize
scaling exponents in the Dicke model,” Europhys.
Lett. 74, 817 (2006).
[30] V. Buzek, M. Orszag, and M. Rosko, “Instability and Entanglement of the Ground
State of the Dicke Model,” Phys. Rev. Lett. 94, 163601 (2005).
[31] O. Tsyplyatyev and D. Loss, “Dicke model: Entanglement as a finite size effect,”
J. Phys.: Conf. Ser. 193, 012134 (2009).
[32] B. M. RodrıguezLara
and R.K.
Lee, “Quantum phase transition of nonlinear light
in the finite size Dicke Hamiltonian,” J. Opt. Soc. Am. B 27, 2443 (2010).
[33] R. A. Robles Robles, S. A. Chilingaryan, B. M. RodrıguezLara,
and R.K.
Lee,
“Ground state in the finite Dicke model for interacting qubits,” Phys. Rev. A 91,
033819 (2015).
[34] S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today 50, No. 7,
36 (1997).
[35] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced
transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633 (2005).
[36] C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical
information storage in an atomic medium using halted light pulses,” Nature 409,
490 (2001).
[37] T. Chaneliere, D. N. Matsukevich, S. D. Jenkins, S.Y.
Lan, T. A. B. Kennedy, and
A. Kuzmich, “Storage and retrieval of single photons transmitted between remote
quantum memories,” Nature 438, 833 (2005).
[38] M. D. Eisaman, A. Andre, F. Massou, M. Fleischhauer, A. S. Zibrov, and M.
D. Lukin, “Electromagnetically induced transparency with tunable singlephoton
pulses,” Nature 438, 837 (2005).
[39] K. Honda, D. Akamatsu, M. Arikawa, Y. Yokoi, K. Akiba, S. Nagatsuka, T. Tanimura,
A. Furusawa, and M. Kozuma, “Storage and retrieval of a squeezed vacuum,”
Phys. Rev. Lett. 100, 093601 (2008).
[40] J. Appel, E. Figueroa, D. Korystov, M. Lobino, and A. I. Lvovsky, “Quantum
memory for squeezed light,” Phys. Rev. Lett. 100, 093602 (2008).
[41] Y.L.
Chuang and R.K.
Lee, “Conditions to preserve quantum entanglement of
quadrature fluctuation fields in electromagnetically induced transparency media,”
Opt. Lett. 34, 1537 (2009).
[42] Y.L.
Chuang, I. A. Yu, and R.K.
Lee, “Quantum theory for pulse propagation
in electromagneticallyinducedtransparency
media beyond the adiabatic approximation,”
Phys. Rev. A 91, 063818 (2015).
[43] Y.L.
Chuang, R.K.
Lee, and I. A. Yu, “Opticaldensityenhanced
squeezedlight
generation without optical cavities,” Phys. Rev. A 96, 053818 (2017).
[44] Y.L.
Chuang, R.K.
Lee, and I. A. Yu, ”Generation of Quantum Entanglement
based on Electromagnetically Induced Transparency Media,” arXiv: 1906.12025
(2019).
[45] M. Hayn and T. Brandes, “Thermodynamics and superradiant phase transitions in
a threelevel
Dicke model,” Phys. Rev. E 95, 012153 (2017).
[46] K. R. Brown, K. M. Dani, D. M. StamperKurn,
and K. B. Whaley, ”Deterministic
optical Fockstate
generation.” Phys. Rev. A 67, 043818 (2003).
[47] H. J. Lipkin, N. Meshkov, and A. J. Glick, “Validity of manybody
approximation
methods for a solvable model. (I). Exact solutions and perturbation theory,”
Nucl. Phys. 62, 188 (1965); N. Meshkov, A. J. Glick, and H. J. Lipkin, “Validity of
manybody
approximation methods for a solvable model: (II). Linearization procedures,”
Nucl. Phys. 62, 199 (1965); A. J. Glick, H. J. Lipkin, and N. Meshkov,
“Validity of manybody
approximation methods for a solvable model: (III). Diagram
summations,” Nucl. Phys. 62, 211 (1965).
[48] Welsch, D. G., Vogel, W., Opatrny, T. (1999). “II Homodyne detection and
quantumstate
reconstruction.” Progress in Optics (Vol. 39, pp. 63211).
Elsevier.
[49] Lvovsky, A. I. (2004). “Iterative maximumlikelihood
reconstruction in quantum
homodyne tomography.” Journal of Optics B: Quantum and Semiclassical Optics,
6(6), S556
[50] Leonhardt, U., Paul, H., d’Ariano, G. M. (1995).“ Tomographic reconstruction of
the density matrix via pattern functions. Physical Review A, 52(6), 4899.
[51] Smithey, D. T., Beck, M., Raymer, M. G., Faridani, A. (1993). “Measurement
of the Wigner distribution and the density matrix of a light mode using optical
homodyne tomography: Application to squeezed states and the vacuum. Physical
review letters, 70(9), 1244.
[52] d’Ariano, G. M., Macchiavello, C., Paris, M. G. A. “ Detection of the density
matrix through optical homodyne tomography without filtered back projection.”
Physical Review A, 50(5), 4298.(1994).
[53] Tiunov, E. S., Tiunova, V. V., Ulanov, A. E., Lvovsky, A. I., “ Fedorov, A. K.
“ Experimental quantum homodyne tomography via machine learning.” Optica,
7(5), 448454.(
2020).
[54] Gardiner, C., Zoller, P., Zoller, P..“ Quantum noise: a handbook of Markovian and
nonMarkovian
quantum stochastic methods with applications to quantum optics.”
Springer Science and Business Media. (2004)
[55] Vogel, K., Risken, H.. “Determination of quasiprobability distributions in terms
of probability distributions for the rotated quadrature phase.” Physical Review A,
40(5), 2847. (1989)
[56] Titchmarsh, E. C. . “ Some integrals involving Hermite polynomials.” Journal of
the London Mathematical Society, 1(1), 1516.
(1948)
[57] Shepp, L. A., and Logan, B. F. (1974). “The Fourier reconstruction of a head section.”
IEEE Transactions on nuclear science, 21(3), 2143.