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3
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84927307669
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M. Born and K. Huang, Dynamical Theory of Crystal Lattices, (Oxford University Press, New York, 1954), reprinted in 1985;
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6
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84927307668
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J. L. Birman in Ref. 6.
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7
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84927307667
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Polaritons, Proceedings of the First Taormina Research Conference on the Structure of Matter, edited by E. Burstein and F. De Martini (Pergamon, New York, 1972); S. I. Pekar, Crystal Optics and Additional Light Waves (Benjamin-Cummings, New York, 1983); R. Loudon, in Nonlinear Optics with Polaritons, Proceedings Society Italiana di Fisica, LXIV, edited by N. Bloembergen (North-Holland, Amsterdam, 1977).
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8
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0343035509
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edited by, M. D. Sturge, E. I. Rashba, North-Holland, Amsterdam
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(1982)
Excitons
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11
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84927307666
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and Ref. 5.
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20
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84927263536
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(1969)
ibid.
, vol.182
, pp. 945
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24
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84927307665
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Squeezed and Nonclassical Light, Vol. 190 of NATO Advances Study Institute Series B: Physics, edited by P. Tombesi and R. P. Pike (Plenum, New York, 1989); for a review on squeezing, see, for example, J. Opt. Soc. Am. B 4, No. 10 (1987); J. Mod. Opt. 34, No. 6, (1987).
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25
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84927307664
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See, for instance, J. Opt. Soc. Am. B 4, No. 10 (1987), and references therein.
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27
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84927307662
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E. S. Koteles, in Ref. 6, p. 83.
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29
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84927307661
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R. J. Glauber and M. Lewenstein, in Ref. 13, p. 203.
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32
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84927307660
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and references therein.
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36
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84927307659
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To detect the effects of squeezing, one usually refers to two-quadrature observables by measuring their fluctuations. These oscillate rapidly in time between a very low and a very high value, and for the purpose of detection a procedure of conversion of an oscillating quantity to a constant quantity has to be employed. In ``optical squeezing'' such a procedure is experimentally possible and has been realized in vacuum.13,14 For a polariton two-quadrature operators may also be defined1 but the measurability of their fluctuations inside the medium where the polariton is excited may be rather difficult. However, in some cases may be relatively simpler to measure the non-Poissonian statistics connected with squeezing.
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37
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84927307658
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This is certainly true for any value of rk, when we take the upper sign; for the lower sign, this is true for 0
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39
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84927307657
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Dokl. Akad. Nauk. (SSSR 119, 244 (1958)
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42
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84927307656
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We restore the notation accordingly: γ hat1-> γ hat+k, γ hat2-> γ hat-k, α1-> αk+, α2-> αk-, β1-> βk+, β2-> βk-. See also Eq. (2.17).
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43
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84927307655
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For different wave vector magnitudes we include the k dependence on the squeeze factor and angle r and cphi.
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44
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84927307654
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Although in different contexts, results that relate the squeezing to the dielectric properties of a medium have independently been obtained by R. Glauber and M. Lewenstein, Ref. 18, and by I. Abram, Ref. 17. However, unlike these works, in this paper we analyze nonclassical properties in a resonant material—essential to create a polariton.
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45
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84927307653
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To simplify the notation, we suppress the sign ``+'' in the +k subindexes where does not create confusion.
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47
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84927307652
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It is important to stress that the electromagnetic field leaking off the surface, unlike the free transmitted field propagating in vacuum, is described by the radiative component of a polariton mixed wave excited inside the crystal. See, e.g., A. D. Boardman, Electromagnetic Surface Modes (Wiley, New York, 1982). The appropriate conceptual framework that permits one to understand this distinction is the extinction theorem [, ] extended to the quantum optics regime: Accordingly, the evanescent field is in our case the portion (dipole field) of the inside field that does not extinguish the vacuum incident field. This is discussed in detail in Ref. 15.
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(1916)
P.P. Ewald, Ann. Phys. (Leipzig)
, vol.49
, pp. 1
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48
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84927307651
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These leaky waves must not be confused with surface polariton waves that are discussed, e.g., in V. M. Agranovich and D. L. Mills, Surface Polaritons (North-Holland, Amsterdam, 1982); see also Ref. 33.
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50
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84927307649
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Only the principal causes of distortion in the detection of polariton light statistics by this direct method are considered here, whereas a more detailed discussion is given in Ref. 33.
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57
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84927374128
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The two distinct coefficients A1k, A2k manifestly designate the resonant and nonresonant parts of the interaction that couples photons and excitons in a polariton. The coefficient Bk relates to the contribution of the nonresonant part of the ``photon-photon'' coupling (a hatka hatkdag) to the single-photon dressed energy, whereas Bksprime, distinct from Bk, relates to the resonant part ( a hatka hat-k) of the same interaction. These terms and H.c. physically originate from the interaction between the electromagnetic field and polarizable electrons.12 Similarly, for Ck and Cksprime: They are associated to the nonresonant (b hatkb hatkdag) and resonant ( b hatkb hat-k) parts of the ``exciton-exciton'' coupling. These terms and H.c. arise from the exciton dispersion relation. For Frankel excitons, the transfer of excitation from site to site gives rise to such a term. For Wannier excitons, they are related to the effective mass of the exciton, although we do not account [Truncated]
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(1932)
Ann. Phys. (Leipzig)
, vol.13
, pp. 905
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58
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36149023453
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Taft [
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in L. Apker and Taft [Phys. Rev. 79, 964 (1950)
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(1950)
Phys. Rev.
, vol.79
, pp. 964
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Apker, L.1
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59
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84927307647
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87, 814 (1951)];
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60
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84927307646
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or in F. Seitz [The Modern Theory of Solids (McGraw-Hill, New York, 1940)]. Also see M. Artoni, Ph.D. thesis, City University of New York, 1991.
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61
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33845331942
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A discussion on the group structure of other polariton Hamiltonians may be found, e.g., in S. Kim and J. Birman [
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A discussion on the group structure of other polariton Hamiltonians may be found, e.g., in S. Kim and J. Birman [Phys. Rev. B 38, 6, 4291 (1988)].
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(1988)
Phys. Rev. B
, vol.38
, Issue.6
, pp. 4291
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62
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The μ hat's and η hat's represent the same operator: We introduce two different symbols purely for clarity.
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64
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Especially, e.g., in the second case where for a paramplifier, zeta contains the appropriate pump field which has apparntly no counterparts in the present physical system.
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65
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0004424057
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The propagating field component of the polariton is discussed, e.g., by
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(1981)
Phys. Rev. B
, vol.24
, pp. 884
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Skettrup, T.1
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66
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0001632492
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A photon in the crystal can transform directly into an exciton, provided that they both have the same energy and wave vector. If the exciton is not scattered by a phonon or some other defects, energy ``oscillates'' back and forth between exciton and photon owing to energy–wave-vector conservation as discussed, e.g., in Ref. 10. The propagating field of the polariton describes this ``intrinsic phase'' of the polariton, and the oscillations above can be ascribed to the oscillations of the mixed boson c hat. The latter are estimated directly from OMEGA [cf. Eq. (C1)] and for an exciton polariton in CdS at k = k0, hbar-1Ω app 1015 sec-1. This rate of energy exchange has been evaluated in other contexts and is of the same order of magnitude [cf., and Dynamical Processes in Solid State Optics, edited by R. Kubo (Benjamin, New York, 1967), Part I].
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(1968)
Phys. Rev.
, vol.166
, pp. 769
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Tait, W.C.1
Weheir, R.L.2
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67
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84927307643
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If | 0 > == | 0ph> | 0excrangle, then a hat+-k | 0 > = b hat+-k | 0 > =0 and from Eq. (3.2), c hat+-k | 0 > = 0.
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68
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Here t = 0 is a reference time.
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72
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Actually, we use trial functions so as to express the three free c functions in terms of one of them, say, e.g., Bk (Ck) and Cksprime (Ck), and we then construct Ck by inverting Eq. (3.13)—now a function of Ck only—taking curlepk as the experimental energy. This fitting procedure by which we give the parametrization of H hatpol in (3.1) is not unique.
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73
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An analogous treatment holds for the conjugate quadrature X hatkq.
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