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arXiv:1601.01511

Lasing at arbitrary frequencies with atoms with broken inversion symmetry and an engineered electromagnetic environment

Michael Marthaler, Martin Koppenhöfer, Karolina Słowik, Carsten Rockstuhl

Published Jan 7, 2016• 2 citations
arXivHTMLPDF

Abstract

With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions become possible. We assume furthermore that the electromagnetic environment has a spectrum with a single sharp resonance, which serves as a lasing cavity. Additionally, the electromagnetic environment should have a very broad resonance around a frequency which differs form the sharp resonance. We use the polaron transformation and derive a rate equation to describe the dynamics of such system. We find that lasing at the frequency of the sharp mode is possible, if the energy difference of the atomic transition is similar to the sum of the frequencies of both peaks in the spectral function. This allows for the creation of lasing over a large frequency range and may in perspective enable THz lasing at room temperature.

DOI
10.48550/arxiv.1601.01511

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With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions become possible. We assume furthermore that the electromagnetic environment has a spectrum with a single sharp resonance, which serves as a lasing cavity. Additionally, the electromagnetic environment should have a very broad resonance around a frequency which differs form the sharp resonance. We use the polaron transformation and derive a rate equation to describe the dynamics of such system. We find that lasing at the frequency of the sharp mode is possible, if the energy difference of the atomic transition is similar to the sum of the frequencies of both peaks in the spectral function. This allows for the creation of lasing over a large frequency range and may in perspective enable THz lasing at room temperature.
We consider a two-level system with both a transversal and a longitudinal coupling to the electromagnetic field of a resonator. Using a polaron transformation, this Hamiltonian can be mapped onto a Jaynes-Cummings Hamiltonian with generalized field operators acting on the electromagnetic field in the resonator. In contrast to the usual ladder operators aaa and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$, these operators exhibit a nonmonotonous coupling strength with respect to the number nnn of photons in the resonator. In particular, there are roots of the coupling between qubit and resonator at certain photon numbers n0{n}_{0}n0​. We show that this effect can be exploited to generate photon-number squeezed light, characterized by a Fano factor $F\ensuremath{\ll}1$, with a large number of photons (e.g., of the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$).
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.
Exposed to a strong electromagnetic field, a two-level system with broken inversion symmetry radiates at the Rabi frequency ΩR. This can be used to generate terahertz waves [Phys. Rev. Lett.102, 023601 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.023601]. We show that a system composed of two tunneling-coupled asymmetric two-level systems radiates at frequency (ξ1−ξ2)2+ΩR2, where energies ℏξ1 and ℏξ2 characterize the tunneling interaction. This opens the possibility of tuning the terahertz spectrum in a considerable range. We also show that for particular amplitudes of the driving field, the emission at frequency (ξ1−ξ2)2+ΩR2 is suppressed.
Lasing [1, 2] and superradiance [3‐5] phenomena are currently enjoying a renaissance as research topics in atomic physics. Fundamentally based on the interaction of matter with an electromagnetic (light) field, the atomic dipoles in a “lasing medium” collectively emit into selected modes of the electromagnetic field and thereby create an amplified and coherent source of light. Present-day lasers use di erent types of gain media and cover a wide range of output frequencies for application in both, fundamental research and industry. A recent string of papers has reported on superradiance [6, 7] and lasing-type instabilities using Bose gases of various type (thermal atoms [8, 9], photon gases [10] and Bose-Einstein condensed atoms [11‐14]) in optical cavities. Buoyed by experimental control over essentially single excitation quanta of atoms and photons [15‐19] in cavity quantum electrodynamics, these works o er intriguing prospects for the next wave of experiments on strongly interacting light-mattter systems including a new regime where unexpected many-body and quantum fluctuation e ects of the lasing medium may become visible. Bohnet et al. [20] recently operated a superradiant “bad-cavity” laser in the few-photon regime based on coherent oscillations of the inter-atomic, collective dipole of the ultracold atoms in the cavity [21]. In this paper, we point out that a quantum degenerate Fermi gas has remarkable features as a lasing medium in a transversally driven cavity as sketched in Fig. 1. We show that the quantum statistics of the Fermi gas puts the coupled cavity+atoms system generically close to superradiance threshold as a consequence of the Pauli exclusion principle (“Pauli pressure”). Physically, this arises from enhanced scattering of fermions between di erent points on the Fermi surface with radiusjkFj by exchanging relatively large photon momenta Q from the cavity as illustrated in Fig. 1. By changing the power of the pump laser at a given density of the Fermi gas, the lasing transition is concomitant with the spontaneous formation of a charge density wave oscillating with 1=Q in real space. Tuning the ratiojkFj=jQj allows to generate a cavity spectrum with “broadband light” in certain spectral ranges or, for energies outside the particle-hole continuum of the fermions, light with relatively narrow linewidth. The normal mode splitting of the cavity by a single atom is completely replaced by many-body Ω |kF| Q
Abstract Simultaneous strong coherent pumping of the two transitions of a V-level atom with very different decay rates has been predicted to create almost perfect inversion on the narrower transition. Using the example of the blue and red transitions in Strontium we show that for suitable operating conditions the corresponding resonant gain can be used to continuously operate a laser on the narrow transition. In particular, for a strong detuning of the pump field with respect to the narrow transition, coherent laser emission occurs close to the bare atomic transition frequency exhibiting only a negligible contribution from coherent pump light scattered into the lasing mode. Calculations of the cavity output spectrum show that the resulting laser linewidth can get much smaller than the bandwidth of the pump light and even the natural linewidth of the narrow atomic transition. Its frequency is closely tied to the atomic transition frequency for properly chosen atom numbers. Simulations including atomic motion show Doppler cooling on the strong transition with minor motion heating on the lasing transition, so that continuous laser operation in the presence of a magneto-optical trap should be possible with current experimental technology.