Two-photon Lasing Research Articles

Noise quenching in lasers and masers by strong coherent pumping.

An intense single-mode correlated-spontaneous-emission laser or maser can be realized by driving the active atoms coherently with an injected external field. The scheme involves single-photon transitions unlike the two-photon or quantum-beat correlated-emission lasers that utilize correlations between successive photon-cascade emissions or between simultaneous emissions into modes of the field. Quenching of both the amplitude and phase noise and, in certain cases, squeezing of the amplitude fluctuations are found.

Two-photon gain and lasing in strongly driven two-level atoms.

Driven two-level atoms are shown to exhibit strong, resonantly enhanced, two-photon gain. This gain, unlike that observed in nonlinear mixing processes, is not constrained by a phase-matching condition involving the pump beam. Physically, the gain can be associated with inverted two-photon transitions between dressed states or multiphoton stimulated Raman scattering, and it may be useful in the realization of a two-photon laser. Comparison with the well-known single-photon gain found in the same system is made.

Theory of the degenerate two-photon laser.

We derive the equation of motion for the field density matrix of the degenerate two-photon laser under conditions of two-photon resonance starting from the full microscopic Hamiltonian. Our results are compared with the corresponding quantities obtained from the standard effective Hamiltonian. As we have shown for the nondegenerate case, the full diagonal density-matrix equations tend to the effective Hamiltonian density-matrix equations in an appropriate limit, but the equations of motion for the off-diagonal elements do not coincide. The equations obtained using a more accurate form of the effective Hamiltonian, in which Stark shifts are included, do agree. In this paper we concentrate on the photon-number distribution and the nature of the phase transition that takes place in the neighborhood of the two-photon lasing transition threshold. We determine the steady-state mean photon numbers and consider the stability of the solutions. A solution is found where the mean photon number is zero, but this is found to be a stable solution only for sufficiently weak pumping, whereas in the standard effective Hamiltonian approach it is always stable. As the pumping strength is increased, a range of detunings is reached in which there are two stable solutions. The amplitude of the zero-photon peak diminishes very rapidly as the pumping strength increases. Finally, for sufficiently large detunings, a single, stable, steady-state solution is obtained. The nature of the phase transition is illustrated by presenting plots of the photon-number distribution against detuning and pumping rate. The photon-number fluctuations about the mean are also discussed.

Off-resonance operation of inhomogeneously broadened two-photon lasers.

We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.

Fokker-Planck equation and allowance for quantum fluctuations in the theory of excitons and biexcitons of high density

The methods of the quantum theory of fluctuations and damping are used to obtain a master equation for the density matrix of Bogolyubov-coherent excitons, photons, and biexcitons in solids. Glauber's P representation is used to derive a Fokker-Planck equation for the system of coherent quasiparticles. Conditions are found for two-photon lasing biexcitons in the case of exciton-biexciton conversion. It is shown that transition from the disordered to the ordered phase is equivalent to a phase transition of the first kind.

Theory of two-photon lasers I

We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.

Theory of two-photon lasers II

Theory of two-photon lasers II

Theory of two-photon lasers III

Theory of two-photon lasers III

On nonclassical effects in two-photon optical bistability and two-photon laser

We analyse the fluctuations at steady state in the good quality cavity case in two-photon lasers with running wave and two-photon absorptive optical bistability in a ring cavity. In the case of two-photon laser we do not find any nonclassical effect, contrary to expectations. On the other hand, in two-photon optical bistability we find squeezing and antibunching in the low transmission branch. The maximum reduction of fluctuations that can be obtained is slightly larger than by a factor of two.

Effect of cooperative atomic interactions on photon statistics in a two-photon laser

The effects of cooperative atomic interactions on photon statistics in a single mode as well as two-mode two-photon lasers are studied using the equation of motion for the reduced-density operator for the field. The steady-state solution of this equation of motion is used to determine the photon number distribution. The importance of the cooperative effects is discussed.

Infrared-microwave two-photon spectroscopy with13C16O2 and12C18O2 lasers of the ν2-band of ammonia

A tunable microwave frequency was added to, or subtracted from fixed frequency13C16O2 and12C18O2 laser lines using the nonlinearity of molecular absorptions. In this way the frequency of 30 transitions of the ν2-band of ammonia were measured with an accuracy of ±0.0005 cm−1. A further four transitions were measured with an accuracy of ±0.0001 cm−1 by saturating the two-photon transition and observing the Lamb dip. For laser lines up to 11 GHz off-resonant with in frared transitions Doppler-limited signals were observed with microwave power densities of only 10 mW/cm2 using a wide-band intracavity cell.

Two-photon coherent states of the radiation field

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.

States that give the maximum signal-to-quantum noise ratio for a fixed energy

Under a radiation power constraint, the maximum signal-to-quantum noise ratio obtainable for any state of a radiation field is found. This maximum value is achieved by the two-photon coherent states introduced previously to describe two-photon lasers.

Generalized coherent states and the statistics of two-photon lasers

Stimulated two-photon emission is proposed as a possible mechanism for the generation of “generalized coherent states”, which have useful quantum properties not available in ordinary coherent states.