Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Laser Physics

A scheme for ultrashort X-ray lasing without inversion

Doron Braunstein, R. Shuker

Published Feb 1, 2006• 1 citation
Publisher

Abstract

A scheme for obtaining a laser without inversion in the deep X-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in the Ar 8+ system. In this system, conventional lasing with population inversion in a neonlike scheme is used. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. The ground level is incoherently pumped into the highest level, while the latter is incoherently depumped into the ground level, at a different adjustable rate. A detailed density matrix calculation of the ladder configuration is performed [3], and the conditions under which the system exhibits inversionless gain, as well as regular gain, are derived. Numerical calculations in the bare state picture exhibits gain without inversion both at resonance and at the generalized Rabi side bands. The probe lineshape is shown to be constructed of two symmetrical dispersionlike features each centered at the generalized Rabi side bands. This is evidence of the quantum interference occurring at these locations and the basis for the gain without inversion.

DOI
10.1134/s1054660x06020186

Related papers

X-ray laser without inversion in a three-level ladder system

Doron Braunstein, R. Shuker

A scheme for obtaining laser in the deep x-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in ${\mathrm{Ar}}^{+8}$ system. In this system, conventional lasing with population inversion has been obtained in a neonlike fashion. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. This will be selected to best match the frequency needed for the transition from lower level of the present x-ray lasing to the ground state. Numerical calculations in the bare state picture exhibit possible gain at resonance, and at the Rabi side bands, for appropriate choice of system parameters, i.e., the strength of the driving field, the strength of the incoherent pump that provides the required energy needed for the inversionless amplification and the deexcitation rate. The latter rate is detrimental to lasing as it increases. It is quite interesting to note that the system exhibits surprisingly high stability for gain without inversion even for quite high rate of the incoherent deexcitation processes. Real and imaginary parts of the coherences were also obtained for detuned drive and probe fields. These provide insight into the role played by the quantum interference. The present theoretical calculations give high confidence in the quantum interference process as a candidate for realizing very short wavelength laser.

Physical Review A•Jul 15, 2003•28 citations

Highly non-resonant lasing without inversion gain in a ladder scheme

Doron Braunstein, Gennady A. Koganov, Ella Smolik +2 more

Abstract We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ –Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The whole γ –Λ plane is divided into four areas: gain-inversion, absorption-no inversion, gain without inversion and absorption with inversion. The first two are usual regimes of incoherently pumped lasers, while the last two stem from the quantum interference phenomena. We analyse the parameter areas where such quantum regimes are possible. The exact numerical solution of the time-dependent master equation shows that keeping counter-rotating terms (no rotating wave approximation) gives rise to new spectral features in the form of additional peaks at combination frequencies. Actually the considered system works as a coherent frequency up-converter.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 21, 2020•2 citations

Inversionless lasing with self-generated driving field

Alexey A. Belyanin, Cleo L. Bentley, Federico Capasso +2 more

We propose and study resonant ladder schemes of inversionless lasing on a fast-decaying transition when the population inversion is not possible or very difficult to achieve. The driving field on a neighboring, slowly decaying transition is not imposed externally, but is self generated in the same active medium. Inversionless lasing in such schemes avoids the problem of driving-field absorption and leads to considerable reduction in the required pumping rate. Applications of such schemes include inversionless ultraviolet and soft x-ray lasing in gas lasers and inversionless generation of coherent mid/far-infrared emission on intersubband (interlevel) transitions in multiple quantum-well or quantum-dot laser diodes.

Physical Review A•Jun 12, 2001•27 citations

Lasing without inversion in the absence of a coherent coupling field

Gautam Vemuri, Kashyap V. Vasavada, G. S. Agarwal

We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.

Physical Review A•Oct 1, 1995•40 citations

Counterintuitive versus regular inversionless gain in a coherently prepared ladder scheme

Doron Braunstein, Ella Smolik, Gennady A. Koganov +2 more

In this research we study lasing without population inversion from a three-level atom interacting with two laser fields, in the ladder or cascade scheme. We investigate counterintuitive sequencing as well as regular sequencing of the time of laser fields application. In a counterintuitive sequence scheme a short probe pulse is introduced prior to the application of the coupling field, in contrast, to a standard sequence scheme, where both fields are introduced at the same time. The influence of varying the probe pulse width and time delay between the initiation of probe and coupling fields on transient probe gain is investigated. The calculations indicate the potential of producing gain without inversion via counterintuitive sequence scheme.

Laser Physics•May 25, 2011•1 citation

Dressed states analysis of lasing without inversion in a three-level ladder system: the steady-state regime

Doron Braunstein, R. Shuker

A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.

Journal of Physics B Atomic Molecular and Optical Physics•May 26, 2009•12 citations
A scheme for obtaining a laser without inversion in the deep X-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in the Ar 8+ system. In this system, conventional lasing with population inversion in a neonlike scheme is used. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. The ground level is incoherently pumped into the highest level, while the latter is incoherently depumped into the ground level, at a different adjustable rate. A detailed density matrix calculation of the ladder configuration is performed [3], and the conditions under which the system exhibits inversionless gain, as well as regular gain, are derived. Numerical calculations in the bare state picture exhibits gain without inversion both at resonance and at the generalized Rabi side bands. The probe lineshape is shown to be constructed of two symmetrical dispersionlike features each centered at the generalized Rabi side bands. This is evidence of the quantum interference occurring at these locations and the basis for the gain without inversion.
A scheme for obtaining laser in the deep x-ray regime is proposed based on the principle of gain without inversion. A ladder scheme is proposed in Ar+8{\mathrm{Ar}}^{+8}Ar+8 system. In this system, conventional lasing with population inversion has been obtained in a neonlike fashion. This lasing field is proposed for the drive field on the higher transition of the ladder. A coherent field obtained in the high harmonics ultrashort laser provides the probe field to be amplified. This will be selected to best match the frequency needed for the transition from lower level of the present x-ray lasing to the ground state. Numerical calculations in the bare state picture exhibit possible gain at resonance, and at the Rabi side bands, for appropriate choice of system parameters, i.e., the strength of the driving field, the strength of the incoherent pump that provides the required energy needed for the inversionless amplification and the deexcitation rate. The latter rate is detrimental to lasing as it increases. It is quite interesting to note that the system exhibits surprisingly high stability for gain without inversion even for quite high rate of the incoherent deexcitation processes. Real and imaginary parts of the coherences were also obtained for detuned drive and probe fields. These provide insight into the role played by the quantum interference. The present theoretical calculations give high confidence in the quantum interference process as a candidate for realizing very short wavelength laser.
Abstract We show that it is possible to get gain without inversion at high frequency in a three-level ladder type scheme driven by a single driving laser. The transition from the ground state to first excited state is driven by a low-frequency resonant laser field. The next excited state lies far above the first one; therefore its resonant frequency can be much higher than that of the lower transition, and hence one should go beyond the most commonly used rotating wave approximation consisting of retaining only resonant terms (slowly oscillating) in the Hamiltonian. We solve the master equation, both analytically (under proper approximations) and numerically, with the full Hamiltonian keeping counter-rotating highly non-resonant terms. We show a dressed state picture explaining spectral features of gain-absorption profiles. Also we present a kind of phase diagram in the plane γ –Λ, where γ and Λ are spontaneous emission rate and incoherent pumping rate, respectively. The whole γ –Λ plane is divided into four areas: gain-inversion, absorption-no inversion, gain without inversion and absorption with inversion. The first two are usual regimes of incoherently pumped lasers, while the last two stem from the quantum interference phenomena. We analyse the parameter areas where such quantum regimes are possible. The exact numerical solution of the time-dependent master equation shows that keeping counter-rotating terms (no rotating wave approximation) gives rise to new spectral features in the form of additional peaks at combination frequencies. Actually the considered system works as a coherent frequency up-converter.
We propose and study resonant ladder schemes of inversionless lasing on a fast-decaying transition when the population inversion is not possible or very difficult to achieve. The driving field on a neighboring, slowly decaying transition is not imposed externally, but is self generated in the same active medium. Inversionless lasing in such schemes avoids the problem of driving-field absorption and leads to considerable reduction in the required pumping rate. Applications of such schemes include inversionless ultraviolet and soft x-ray lasing in gas lasers and inversionless generation of coherent mid/far-infrared emission on intersubband (interlevel) transitions in multiple quantum-well or quantum-dot laser diodes.
We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.
In this research we study lasing without population inversion from a three-level atom interacting with two laser fields, in the ladder or cascade scheme. We investigate counterintuitive sequencing as well as regular sequencing of the time of laser fields application. In a counterintuitive sequence scheme a short probe pulse is introduced prior to the application of the coupling field, in contrast, to a standard sequence scheme, where both fields are introduced at the same time. The influence of varying the probe pulse width and time delay between the initiation of probe and coupling fields on transient probe gain is investigated. The calculations indicate the potential of producing gain without inversion via counterintuitive sequence scheme.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.