Search Results (32 total)

A recent work on two-photon fluorescence is extended by considering the pump field to be a coherent state, which represents a laser field operating well above threshold. The dynamical conditions are investigated under which the two-photon spectrum gives rise, in addition to a Lorentzian line shape at the pump frequency, to two Voigt spectral sideband profiles. Additional conditions are found under which the Voigt profile behaves like either a Gaussian or a Lorentzian line shape.

We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2∕3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4∕5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.

The Raman interaction of atoms singly traversing a two-mode cavity constitutes a quantum-cloning machine for coherent states. The quality of the two identical output coherent states is independent of the initial, albeit different, coherent state, initially present inside the cavity. The cloning of nonorthogonal states indicates that the entanglement of the output states for an arbitrary initial state is the essence of the no-cloning theorem.

The dynamics of an exact two-photon Hamiltonian is used to study the time evolution of an initially disentangled pure state of the atom-field system as it goes through cycles of entanglement separated by instances of disentanglement. For specific initial states of the electromagnetic field, the output state is a pure quantum superposition of a squeezed vacuum state and an orthogonal, odd-photon-number state. The odd-photon-number state, which is not a squeezed state, exhibits both nonclassical sub-Poissonian and classical super-Poissonian photon statistics. In the latter case the quantum superposition resembles a macroscopic superposition state. Conditions are obtained on the atom-cavity interaction time for such states to represent the steady states in the injection in a high-Q cavity of a monoenergetic, low-density beam of three-level atoms in a coherent state.

A Comment on the Letter by Hiromi Ezaki, Phys. Rev. Lett. 83, 3558 (1999). The authors of the Letter offer a Reply.

Starting from a three-level atom coupled to two modes of radiation field, we derive a Raman-coupled Hamiltonian by a unitary transformation, evaluated perturbatively in coupling constants. The Rabi oscillation frequency and the collapse and revival times of the atomic coherence are found to have strikingly different photon-intensity dependence than those found previously.

We investigate the relaxation of a two-level system (TLS) in the golden-rule approximation by taking into account phonon-mediated interactions between TLS’s.

S. Jasty, M. Al-Naghy, and M. de Llano recently presented [Phys. Rev. A 35, 1376 (1987)] an argument to justify the weak divergence of the pressure at random close packing for a classical continuous system with hard cores. Their analysis is based on the behavior of the equilibrium canonical partition function at random close packing. Therefore this approach is erroneous owing to the nonequilibrium nature of the glassy state.

A method, based on the first few virial coefficients, is used to generate the pressure P of a classical d-dimensional hard-core system at arbitrary density ρ—the method is exact for d=1. The equation of state reproduces all the virial coefficients used on expanding P/k_BT about ρ=0. Also, P/ρ_ck_BT→R/(1-ρ/ρ_c) as ρ→ρ_c and ∂(P/k_BT)/∂ρ>0 for 0<eqρ<ρ_c. As the order of the approximation increases, the position ρ_c of the simple pole approaches the density ρ₀ of closest packing and the residue R increases beyond the value of the spatial dimensionality d of the system. The equation of state is in rather good agreement with the molecular-dynamics results especially for the case of hard disks as expected.

It is shown that the divergence of the pressure at the close-packed volume for the metastable supercooled fluid branch may be less singular than that of a first-order pole—the result of the free-volume theory. Such weaker singularity gives a possible explanation of why the numerical values found for the close-packed volume are always less than Bernal’s random close-packing volume.

The stability of the critical solutions of Jones's linear differential equation against the addition of a nonlinear term is studied. The class of correlation functions considered include those which do not possess a power-law decay at criticality, but which are of scaling form.

It is shown that the existence of a critical point, with γ≤2ν, of the Yvon-Bron-Green equation depends sensitively on the very-short-distance part of the net correlation function h(r). However, if γ>2ν, then the asymptotic (r→∞) behavior of h(r) suffices. Also, the approximate nonlinear differential equation describing the long-distance part of the full integral equation allows for a critical point with positive net correlations for d=3, provided that the scaling or long-ranged part of h(r), h_c(r), vanishes at the critical point.

A collective-mode description of the dynamical forces among constituents of a hadron by means of distinguishable quasiparticles leads to confinement. Therefore, the confining forces among (Fermi or Bose) constituents are purely a manifestation of the correlations resulting from the statistics of the quasiparticles. Nonetheless, the distinguishable quasiparticles behave in many respects like an ideal Bose (not Fermi) gas.

The main purpose of our work concerns the long-time behavior of initial distributions with diverging second moments and to show that in the mean the behavior is still exponential. We consider solutions F(x,t) of the Boltzmann equation for a Maxwell-like model for which ∫0^∞dx x²F(x,0)=∞ and ∫0^∞dx F(x,0)=∫0^∞dx xF(x,0)=1. It is shown that F(x,t) can be approximated arbitrarily well in the mean by F̅ (x,t) for 0≤t<∞ and F̅ (x,t)≃e^-x[1+Ke^{-t / 3}L₂(x)] as t→∞. Consequently, the Hilbert space of square-integrable functions, viz., ∫0^∞dx F²(x,0)<∞, is complete in the sense of convergence in the mean for 0≤t<∞, and thus the time evolution of initial singularities—for instance, an F(x,0) with δ-function peaks, jump discontinuities, etc.—is not physically meaningful.

It is suggested that the critical-point behavior of the Yvon-Born-Green integral equation for fluids for dimensions d≤4 is described by a net correlation function which vanishes faster than any power of r as r→∞, even though the isothermal compressibility K_T diverges at the critical point.

A temperature-dependent expression for the condensate fraction n₀ for He II based on a model Hamiltonian for superfluids is presented. This gives roughly the same magnitude for n₀ as is observed. The model also suggests the following behavior as T→0 for the roton effective mass μ_r(T)=μ_r(0) [1-(m_He / 24ℏ³cn)(k_BT)²] and the roton minimum energy Δ(T)=Δ(0) [1-(m_He / 24ℏ³cn)(k_BT)²].

A general result for the nonequilibrium distribution function for photons gives a greatest lower bound for the radiation flux spectrum. This inequality allows one to establish, from the recent measurements of the cosmic background radiation, that the observed spectrum arises from the superposition of single sources. Since the primeval fireball may be one of the single sources, it is inferred that the observed spectrum is consistent with a big-bang origin for the universe.

The Bogoliubov treatment of a weakly interacting Bose gas is extended by allowing macroscopic occupation of many single-particle quantum states. This generalization of having more than a single condensed mode gives rise to a nonuniform condensate and is being considered as a possible mechanism for the description of a dense strongly interacting Bose gas at low temperatures. The model with a repulsive δ-function interparticle potential gives an energy spectrum of elementary excitations or quasiparticles with both phonon and roton features. The values obtained for the roton minimum energy Δ and the speed of (first) sound agree reasonably well with inelastic-neutron-scattering data.

It is shown that if the critical-point exponent η vanishes, then phase transitions can exist only in greater than two space dimensions.

A simple extension of the Ornstein-Zernike theory of critical scattering gives rise to correlation functions which do not scale. The critical-point exponents have values η=0 and 2ν≥γ.

A recent charge-symmetric model of the very early stages of a big-bang cosmology is used to derive a value for the fine-structure constant.

A model for particle structure is used to describe the "hadron era" of a charge-symmetric model for the early universe. A value of s≳10⁷k is obtained at t∼10^-7 sec for the fundamental quantity s, the entropy per baryon. This value for s / k is directly related to the magic number of cosmology 10⁴⁰.

The statistical bootstrap models of Hagedorn and Frautschi, modified so that the volume of a hadron is allowed to vary with the temperature, are considered. It is shown that a large class of polynomial solutions for the level density of hadrons is possible. A feature common to polynomial spectra is that the volume of a hadron must vanish as the temperature approaches infinity. The requirement that hadrons have a finite size implies both a maximum temperature and an exponential hadron mass spectrum. Also, the recent formulation in terms of quasiparticles demands an exponential hadron mass spectrum without requiring an asymptotic bootstrap condition. A unique solution, ρ(m)∼m^{-5 / 2}e^mβ as m→∞, is obtained if one assumes the asymptotic bootstrap condition of Hagedorn.