| P. Meystre and M. Sargent III, Elements of Quantum Optics (SpringerVerlag, Berlin, 1991). |
....Fig. 4.1. 5.1.2 Optical Theorem, Asymptotic The general equation (2.3) rewritten below, applies to photon scattering too. j i = j i j s i; 5.6) where j i, j s i and j i are the incident, scattered, and total wave. In this subsection, we treat the radiation eld semiclassically (see, e.g. [45, 46]) For our study of one photon scattering by atoms in ground state, this treatment gives the same result as full quantum mechanical treatment to the eld. The E (r) eld for any eld state j i is de ned as E (r) h0jE (r)j i: 5.7) Besides a normalization factor, the E (r) eld of the single ....
P. Meystre and M. Sargent III, Elements of Quantum Optics (SpringerVerlag, Berlin, 1991).
....represented by the quantized field mode. Then, each atom can exchange at most one photon with the field, and, according to the Jaynes Cummings model [57, 58] the interaction is described by the following unitary operator (in the rotating wave 9 approximation, see, e.g. chapter 14.1 in [59]) # U = e i#(a # a# ) 2.1) Here, a, a are the photon annihilation creation operators, and # = d##u , # = u##d the ladder operators for the two level atom, with upper and lower level respectively. The parameter # = gt int is the vacuum Rabi angle, where t int denotes the ....
....preparation. 6.1 Cavity dissipation Since, under realistic experimental conditions, the cavity field is not perfectly isolated from its environment, the field decays due to the interaction with the cavity walls. This decay can be treated using standard techniques (see, e.g. chapter 15.1 in [59]) the environment is treated as a heat bath at temperature T , which has no memory (Markov approximation) Furthermore, the coupling between cavity field and heat bath is assumed to be weak, and mediated by the photon annihilation and creation operators a and a . Under these general conditions, ....
P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, Berlin, 1990).
....where n k is the number of # particles for the mode with k. So, b (k) is spanned by n # n k =0 . As we saw in (1.25) m N # (k) m V becomes a shift of a frequency from the resonance, so (k) n k 1) in (3. 2) is equal to a general quantized Rabi flopping frequency [MS, WM], which leads us to the spontaneous emission of the photon with a single mode. The eigenstate n k for E n k is in 1 (n k 1) Therefore, for instance, we set #(k) 1 now for the sake of simplicity, and g = 10 , #(k) 10 L , n k = 10 or g = 1, #(k) 10 3L , n k = 10 for ....
Meystre P and Sargent III M 1991 "Elements of Quantum Optics" Springer-Verlag, Berlin Heidelberg
....fl fl y fl z Omega 2 ; 2.32) where fl x = fl(N 1 2 M) fl y = fl(N 1 2 Gamma M) fl z = 1 2 (fl x fl y ) fl 0 = 1 2 (fl y fl z ) fl 2 x 4 Gamma Omega 2 1=2 : 2. 33) The incoherent resonance fluorescence spectrum is produced by fluctuations in the dipole moment [14]. The fluctuations are measured by the variances h Deltaoe i i j hoe 2 i i Gamma hoe i i 2 ; that is: h Deltaoe i i = 1 Gamma hoe i i 2 : 2.34) Now, as suggested by eq. 2.31) the variance in h Deltaoe x i will give rise to features controlled by fl x AE fl: These are broad features, ....
....driven two level atom in a squeezed vacuum, dealing specifically with the hole burning and dispersive profiles at the centre of the spectrum. We note that the hole burning and dispersive spectral features can also take place in the probe absorption spectrum in the absence of a squeezed vacuum [9, 14, 197, 198, 199]. However, these anomalous spectral profiles in the squeezed vacuum have a different origin from the ones studied previously in the standard vacuum situation. The former is induced by nonclassical properties of the squeezed vacuum, whilst the latter is due to additional rapid collisional dephasing ....
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P. Meystre and M. Sargent III, Elements of Quantum Optics, (Springer, Berlin, 1991).
....make contact with the Jaynes Cummings model by assuming a single mode electric field, linearly polarized in the x direction, as would be found in a high Q cavity of volume V , for example. In terms of the standard harmonic oscillator creation and annihilation operators, the field can be written [13]: E = xE Omega (a a y ) sin Kz (47) where E Omega = h Omega =ffl 0 V ] 1 2 is the electric field per photon for an electric field of frequency Omega Gamma In the above, z points along the longitudinal axis of the cavity and K = Omega =c is the magnitude of the corresponding ....
.... The final result has precisely the form of the interaction term for the Jaynes Cummings model: H int = hg(aoe a y oe Gamma ) 50) and we identify the Rabi frequency in our model as: g j Gamma fl x E Omega sinKz hc 3 p m 1 m 2 (51) This corresponds to the usual Rabi frequency [13] g R = Gamma he xi x E Omega h sin Kz (52) on making the identification: fl x = he xi x p m 1 m 2 c 3 (53) which is consistent with the identification for fl made in the previous section (eqn. 17) apart from terms of order (m 1 Gamma m 2 ) m. IV. THE EFFECTIVE ACTION AND ITS ....
P. Meystre and M. Sargent. Elements of Quantum Optics. Springer-Verlag, New York, 1991.
....origin in spontaneous emission, V conserves the purity of the state, while in general V c does not conserve Tr ( r 2 ) 14] As such, it should really be considered a dissipative term, and consistently, be neglected in the coherent regime. In complete analogy with conventional nonlinear optics [21 23] we proceed by introducing slowly varying forward F (r , t ) F e (r , t ) F g (r , t ) and backward B (r , t ) B e (r , t ) B g (r , t ) propagating components of the effective single particle wave function f (r , t ) f (r , t ) F(r,t)e i(kz vt) B (r , t )e i(kz vt) 7) with u ....
P. Meystre and M. Sargent III, Elements of Quantum Optics, Springer, Heidelberg (1991).
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P. Meystre ans M. Sargent III, Elements of Quantum Optics, 2nd ed., Springer, Berlin, 1991
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P. Meystre ans M. Sargent III, Elements of Quantum Optics, 2nd ed., Springer, Berlin, 1991
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Meystre, P., and Sargent, M., III, Elements of Quantum Optics, SpringerVerlag, New York (1990).
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