Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.     

New Developments and Applications in Optical Radiometry

The numerical study of the transmission of laser pulses through a two-photon absorber is given for Fourier-limited and chaotic pulses. The light statistics are investigated through a calculation of the second-order correlation function g ⁽²⁾ which is shown to be very sensitive to the experimental conditions.     

Combination of electromagnetically induced transparency and a mollow absorption spectrum in a degenerate two-level atomic ensemble: F e = 1 ↔ F g = 0

Abstract

We investigate the quantum coherence effects of a closed transition F _e = 1 ? F _g = 0 driven by transverse linearly polarized light field (with [sgrave] ± components) and probed by another transverse, linearly polarized light field. Owing to the competition of two-photon gain and single-photon absorption, the absorption spectrum is shown as a combination of electromagnetically induced transparency (EIT) and Mollow absorption spectrum (MAS). In the degenerate case, the MAS covers the EIT window at the pump-probe detuning centre. In the magnetic field, two single-photon absorption peaks inside the EIT windows appear when the drive Rabi frequency is smaller than the Zeeman splitting while, when the Rabi frequency is larger than the Zeeman splitting, we find four emission peaks due to the two-photon gain. A transition from positive to negative dispersion is obtained, which means a shift between the subluminal and superluminal group velocities.     

Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.     

Lens-less quantum ghost imaging: New two-photon experiments

New types of lens-less two-photon ghost imaging experiments are described that can also be useful for 3D X-ray imaging. In these experimental setups, a CCD array is placed facing a chaotic light source and gated by a photon counting detector that simply counts all randomly reflected photons from an object. A “ghost” image of the object is then observed from the gated CCD. A ghost image of an object can even be observed when the photon path to the photon counting device is obscured. These interesting demonstrations are not only useful for practical applications, such as X-ray lens-less imaging, but are also important from a fundamental point of view. These demonstrations lead to insight regarding the nonclassical two-photon interference nature of thermal light ghost imaging.     

Squeezing Properties and Photon Statistics in Multiphoton Processes with Radiative Damping of the Atomic Levels

Abstract

A model for the master equation of multiphoton processes with radiative damping of the atomic levels is proposed and a matrix method employed to solve exactly the rate equations for the matrix elements of the reduced density operator in the Fock representation. This model has been applied to the study of the low-noise properties of squeezed light in an all-optical transmission link formed from alternating sections of linear and nonlinear attenuating fibre and optical amplifiers. When the attenuators present radiative damping of the atomic levels (the lower atomic state is not the ground state) the signal-to-noise ratio is enhanced with respect to the case in which the lower atomic level is the ground state. The enhancement is improved when the input light is squeezed. The statistical properties of linear and two-photon amplification with an absorption process which exhibits radiative damping have also been analysed for coherent and squeezed inputs. The second-order fluctuations are reduced when radiative damping in the absorption process is considered except in the case of two-photon absorption for small values of the saturation parameter s_a . When the value of this parameter is increased the behaviour of the fluctuations changes and the noise is reduced. These results could be of interest in all-optical transmission links and are improved when the input light is squeezed.     

Trends in optical biomedical imaging

Abstract

Recent progress in the development of optical techniques for non-invasive imaging in biology and medicine is reviewed. We start with some fundamental considerations of light propagation in random media. We then discuss imaging using coherent unscattered light and diffuse light. Microscopic techniques based on one- and two-photon fluorescence are described and several types of nonlinear and time-resolved microscopy are explained. We conclude with some application examples and an outlook.     

Two-photon luminescence imaging of cancer cells using molecularly targeted gold nanorods

We demonstrate the use of gold nanorods as bright contrast agents for two-photon luminescence (TPL) imaging of cancer cells in a three-dimensional tissue phantom down to 75 mum deep. The TPL intensity from gold-nanorod-labeled cancer cells is 3 orders of magnitude brighter than the two-photon autofluorescence (TPAF) emission intensity from unlabeled cancer cells at 760 nm excitation light. Their strong signal, resistance to photobleaching, chemical stability, ease of synthesis, simplicity of conjugation chemistry, and biocompatibility make gold nanorods an attractive contrast agent for two-photon imaging of epithelial cancer.     

Theory of the Polarization Dependence of Two-photon Absorption in Zinc-blende Semiconductors

Abstract

The polarization dependence of two-photon absorption is calculated for several zinc-blende semiconductors. The spectral dependence of the linear/circular dichroism is determined using an isotropic, four-band Kane band-structure model and is shown to have specific features associated with the split-off band. The crystalline orientational dependence is determined using an anisotropic band-structure model obtained by additionally including the next highest upper conduction band set. It is shown that the anisotropic behaviour of the two-photon absorption is small in InSb but is quite substantial in GaAs giving a variation in the two-photon absorption coefficient for linearly polarized light of around 70% at a wavelength of 1 μm.     

Optical state measurement with a two-component probe

Abstract

A state of light which is a superposition of the vacuum and the one-photon number state is the simplest state containing phase information. Recently we have shown how a field in such a state might be generated and here we explore its usefulness as a probe for measuring unknown states of light. We find that this probe can be used reasonably simply both to determine completely some pure states of light and to measure the diagonal and nearest off-diagonal elements of the density matrix in the number state basis and hence to obtain the mean sine and cosine of the phase of an unknown mixed state. We suggest further how a field in a superposition of the vacuum and the two-photon number state might be generated and how this can be used as a probe, both to measure the off-diagonal matrix elements second nearest to the diagonal of a mixed state density matrix and to measure the variance of the cosine and the sine of the phase. We also examine the experimentally more likely case where the probe fields are in mixed states and show how the same information about the unknown state can still be retrieved.     

“Dark” Excited States of Diphenylacetylene Studied by Nonresonant Two-Photon Excitation Optical-Probing Photoacoustic Spectroscopy

Optical probing photoacoustic spectroscopy (OPPAS), a photothermal calorimetric technique, was applied to investigate one-photon forbidden ??dark?? electronically excited singlet states of diphenylacetylene (DPA), belonging to the D _2h point group. When 502?nm light from a pulsed OPO laser was focused into a DPA hexane solution, an acoustic wave was detected as a transient angular deflection of the probe beam (He?CNe laser). The laser power dependence of the OPPAS signal was estimated to be 1.9 ± 0.2, suggesting two-photon absorption for acoustic generation. With the OPPAS technique, we successfully obtained a nonresonant two-photon absorption spectrum of DPA in solution for the first time. The two-photon allowed 1¹ B _3g and 2¹ A _g states were found to be above the one-photon allowed 1¹ B _1u state. These results show that OPPAS is a highly sensitive technique applicable to two-photon absorption spectral measurements of nonfluorescent species.     

Frequency-stabilized 1520-nm diode laser with rubidium 5S(1/2) --> 7S(1/2) two-photon absorption

A 760-nm light source of >10 mW is obtained from a frequency-doubled external-cavity diode laser by use of using an erbium-doped fiber amplifier and a periodically poled lithium niobate waveguide. The 5S(1/2) --> 7S(1/2) two-photon transitions of rubidium are observed with such a light source. This laser frequency is locked to the Rb two-photon transitions with an instability of 10 kHz (1 s). Our experimental scheme provides a compact, high-performance frequency, standard in the S band (1480-1530 nm) for fiber-optic communication and sensing applications.     

Nanoparticles for two-photon photodynamic therapy in living cells

We describe here a nontoxic two-photon photodynamic nanoparticle platform and its cellular application. We demonstrate that the dye's potential toxicity can be circumvented by its permanent encapsulation into a biocompatible nanoparticle polymer matrix; this was examined by dye leaching experiments and confirmed by cell uptake experiments. Infrared two-photon nanoplatform phototoxicity was demonstrated for rat C6 glioma cells, while the controls showed no dark toxicity for these living cells.     

Degenerate two-photon propagation and the oscillating two-stream instability: The general solution for amplitude-modulated pulses

Abstract

Coherent propagation of an optical pulse in a medium with a second-order resonance is investigated when we include both the dynamical Stark effect and a population-dependent refraction index. We show how to obtain the general solution when the incident pulse has no phase-modulation. The amplitude-modulation of the incident pulse can be arbitrary as can be the initial state of the medium. This general solution is reduced to obtaining the solution of an ordinary differential equation and quadratures. For an initially de-excited medium, the solution reduces to that given by Poluektov et al. {I. A. Poluektov, Yu. M. Popov and V. S. Roitberg, 1975, Kvant. Elektron. (Moscow), 2, 1147 [1975, Sov. J. Quant. Electron., 5, 620]}. We give some illustrative examples of solutions for various initial profiles. It is also shown that the oscillating two-stream instability (OTSI) from plasma physics is equivalent to the Maxwell-Bloch equations for degenerate two-photon propagation. We give a solution for the OTSI which contains five arbitrary real functions.     

High-density optical data storage with one-photon and two-photon near-field fluorescence microscopy

A spatially localized photochemical reaction induced by near-field femtosecond laser pulses is demonstrated on a nanometer scale and used for high-density optical data storage. Recorded domains down to 120 and 70 nm are obtained with one-photon and two-photon excitation, respectively. It is shown that the local-field confinement that is due to the quadratic dependence of two-photon excitation on light intensity has the potential to increase the near-field optical storage density.     

Two-photon fluorescence imaging super-enhanced by multishell nanophotonic particles, with application to subcellular pH

A novel nanophotonic method for enhancing the two-photon fluorescence signal of a fluorophore is presented. It utilizes the second harmonic (SH) of the exciting light generated by noble metal nanospheres in whose near-field the dye molecules are placed, to further enhance the dye's fluorescence signal in addition to the usual metal-enhanced fluorescence phenomenon. This method enables demonstration, for the first time, of two-photon fluorescence enhancement inside a biological system, namely live cells. A multishell hydrogel nanoparticle containing a silver core, a protective citrate capping, which serves also as an excitation quenching inhibitor spacer, a pH indicator dye shell, and a polyacrylamide cladding are employed. Utilizing this technique, an enhancement of up to 20 times in the two-photon fluorescence of the indicator dye is observed. Although a significant portion of the enhanced fluorescence signal is due to one-photon processes accompanying the SH generation of the exciting light, this method preserves all the advantages of infrared-excited, two-photon microscopy: enhanced penetration depth, localized excitation, low photobleaching, low autofluorescence, and low cellular damage.     

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

Abstract

We introduce the inverse of the Hermitian operator (ââ ^?) and express the Boson inverse operators â ^?1 and â ^??1 in terms of the operators â, â ^? and (ââ ^?)^?1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as â ²(ââ ^?)^?1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (ââ ^?)^?1 â ², â(ââ ^?)^?1 â and â ²(ââ ^?)^?1 have many similar properties and thus they constitute a family of two-photon annihilation operators.     

Theory of Optical Two-photon Rotary Echo

We present a theory of optical two-photon rotary echo for the case when the direct couplings between the three levels due to spontaneous decay to and from the intermediate state dominate the indirect couplings (collisional, etc.) to the passive levels and the phase-interrupting (P.I.) collisions cannot be ignored. For this situation which generally obtains in the visible/U.V. region which is relevant for many two-photon transient experiments, the ‘two-photon Bloch equations’ with non-resonant intermediate state are non-trivially different from the familiar (two-level) Bloch equations with or without direct coupling. An explicit analytical calculation demonstrates two-photon rotary echo with the usual dependence on the total phase shift. The dependence of the echo peak on pulse delay time is governed by a damping constant in which ‘intensity modification’ involves only the P.I. collision constant and not the spontaneous decay constant in sharp contrast to the one-photon case. For the case of counter-propagating beams, the intensity modified echo damping constant turns out to be especially simple. We suggest that the features unique to the two-photon rotary echo can be usefully exploited for the empirical determination of the polarization decay constant.     

Two-photon interband absorption in size-quantized semiconductor films

The two-photon interband transition probability in a semiconductor film is discussed taking quantum size effects into account. An explicit expression for the transition rate is derived for arbitrary polarization of light with respect to the surface normal. The feasibility of studying the discrete energy levels of electrons in a thin film by means of two-photon spectroscopy is shown.