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Physical Review A

Quantum-mechanical interference in two-photon absorption: A nonlinear analog of the Hanle effect

Gerald J. Diebold

Published Nov 1, 1985• 6 citations
Publisher

Abstract

When an atom is irradiated by two light beams whose sum frequency corresponds to an allowed two-photon transition between two $^{1}\mathrm{S}$ states, no radiation is absorbed if the electric vectors of the two beams are perpendicular to each other. Application of a magnetic field in a direction perpendicular to the plane defined by the two electric vectors permits two-photon absorption to take place. According to quantum theory the effect is interpreted as an interference phenomenon. That is, if no field is applied, the intermediate states are degenerate and the interference is destructive; when a magnetic field is applied, two different paths through intermediate states are possible, permitting population of the upper state. The effect is related to the Hanle effect and likewise provides the basis for an experimental method of determining Land\'e factors.

DOI
10.1103/physreva.32.2739

Related papers

Quantum interference in two-photon absorption: Polarization and magnetic field effects in the (7s )1 S←(5 s2 )1 S transition of atomic Sr

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Quantum-mechanical interference is found in the two-photon excitation of an atomic $^{1}\mathrm{S}$ through the nonresonant sequence $^{1}\mathrm{}^{1}$P\ensuremath{\leftarrow}${\mathrm{}}^{1}$S, since the magnetic sublevels of the intermediate $^{1}\mathrm{P}$ state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s${)}^{1}$S\ensuremath{\leftarrow}(5${\mathrm{s}}^{2}$${)\mathrm{}}^{1}$S transition of atomic Sr excited by two dye lasers operating at different wavelengths.

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The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.

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The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.

•Jun 1, 2006•0 citations

Lasing without inversion and other effects of atomic coherence and interference

Marlan O. Scully, Muhammad Suhail Zubairy

Quantum coherence and correlations in atomic and radiation physics have led to many interesting and unexpected consequences. For example, an atomic ensemble prepared in a coherent superposition of states yields the Hanle effect, quantum beats, photon echo, self-induced transparency, and coherent Raman beats. In fact, in Section 1.4, we saw that the quantum beat effect provides one of the most compelling reasons for quantizing the radiation field. A further interesting consequence of preparing an atomic system in a coherent superposition of states is that, under certain conditions, it is possible for atomic coherence to cancel absorption. Such atomic states are called trapping states †. The observation of nonabsorbing resonances via atomic coherence and interference impacts on the concepts of lasing without inversion (LWI),‡ enhancement of the index of refraction accompanied by vanishing absorption, and electromagnetically induced transparency. In lasing without inversion, the essential idea is the absorption cancellation by atomic coherence and interference. This phenomenon is also the essence of electromagnetically induced transparency. Usually this is accomplished in three-level atomic systems in which there are two coherent routes for absorption that can destructively interfere, thus leading to the cancellation of absorption. A small population in the excited state can thus lead to net gain. A related phenomenon is that of resonantly enhanced refractive index without absorption in an ensemble of phase-coherent atoms ( phaseonium ). In a phaseonium gas with no population in the excited level, the absorption cancellation always coincides with vanishing refractivity.

Cambridge University Press eBooks•Sep 4, 1997•11 citations
When an atom is irradiated by two light beams whose sum frequency corresponds to an allowed two-photon transition between two 1S^{1}\mathrm{S}1S states, no radiation is absorbed if the electric vectors of the two beams are perpendicular to each other. Application of a magnetic field in a direction perpendicular to the plane defined by the two electric vectors permits two-photon absorption to take place. According to quantum theory the effect is interpreted as an interference phenomenon. That is, if no field is applied, the intermediate states are degenerate and the interference is destructive; when a magnetic field is applied, two different paths through intermediate states are possible, permitting population of the upper state. The effect is related to the Hanle effect and likewise provides the basis for an experimental method of determining Land'e factors.
Quantum-mechanical interference is found in the two-photon excitation of an atomic 1S^{1}\mathrm{S}1S through the nonresonant sequence 11^{1}\mathrm{}^{1}11P\ensuremath{\leftarrow}1{\mathrm{}}^{1}1S, since the magnetic sublevels of the intermediate 1P^{1}\mathrm{P}1P state provide multiple pathways for absorption. Depending on the relative polarization of the two incident light beams, the interference can be either constructive or destructive. When the electric vectors of the light beams are linearly polarized and orthogonal, the interference is purely destructive and two-photon transitions are forbidden. Application of an external magnetic field, however, lifts the degeneracy of the intermediate state giving a two-photon absorption rate proportional to the square of the magnetic field strength. These effects are reported for the (7s)1{)}^{1})1S\ensuremath{\leftarrow}(5s2{\mathrm{s}}^{2}s2)1{)\mathrm{}}^{1})1S transition of atomic Sr excited by two dye lasers operating at different wavelengths.
It has recently been shown that certain two-photon transitions can be indiced in atoms by applying a static magnetic field at the intersection of two crossed laser beams. The mechanism involves quantum mechanical interference between different excitation pathways. In this letter it is shown that a similar effect takes place in any highly symmetric molecule such as methane or sulphur hexafluoride belonging to a cubic symmetry group. However, in this case, the effect occurs through a non-linear magneto-optical interaction which is quite distinct from the interference mechanism.
Some atoms fail to absorb radiation even when the energy of the photons corresponds to the difference between two atomic levels. This phenomenon was discovered in 1961 by Ugo Fano of the University of Chicago, who explained it in terms of destructive interference: In the atoms that show this effect, there are two pathways leading to the same excited state, and their sum determines the probability for light to be absorbed. When these amplitudes interfere destructively, no photons are absorbed. One example is the transition from the ground state of helium to the 2s2p state, which lies in the continuum. The atom may be photoionized directly, or it may pass to the continuum via the discrete, autoionizing 2s2p state. As a result there is a window in the absorption spectrum for helium.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.
Quantum coherence and correlations in atomic and radiation physics have led to many interesting and unexpected consequences. For example, an atomic ensemble prepared in a coherent superposition of states yields the Hanle effect, quantum beats, photon echo, self-induced transparency, and coherent Raman beats. In fact, in Section 1.4, we saw that the quantum beat effect provides one of the most compelling reasons for quantizing the radiation field. A further interesting consequence of preparing an atomic system in a coherent superposition of states is that, under certain conditions, it is possible for atomic coherence to cancel absorption. Such atomic states are called trapping states †. The observation of nonabsorbing resonances via atomic coherence and interference impacts on the concepts of lasing without inversion (LWI),‡ enhancement of the index of refraction accompanied by vanishing absorption, and electromagnetically induced transparency. In lasing without inversion, the essential idea is the absorption cancellation by atomic coherence and interference. This phenomenon is also the essence of electromagnetically induced transparency. Usually this is accomplished in three-level atomic systems in which there are two coherent routes for absorption that can destructively interfere, thus leading to the cancellation of absorption. A small population in the excited state can thus lead to net gain. A related phenomenon is that of resonantly enhanced refractive index without absorption in an ensemble of phase-coherent atoms ( phaseonium ). In a phaseonium gas with no population in the excited level, the absorption cancellation always coincides with vanishing refractivity.