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

Physical Review A

Dipole-dipole interaction in optical cavities

Elena V. Goldstein, Pierre Meystre

Published Dec 1, 1997• 68 citations
Publisher

Abstract

At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.

DOI
10.1103/physreva.56.5135

Related papers

Dipole-dipole interaction in cavity QED: The weak-coupling, nondegenerate regime

M. Donaire, J. M. Munõz-Castañeda, Luis Miguel Nieto

We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.

arXiv:1702.00438•Physical Review A•Oct 24, 2017•20 citations

Nonlinear atom optics

Elena V. Goldstein

In contrast to electromagnetic fields, matter-wave fields are intrinsically interacting due to the presence of atom-atom collisions. Hence, matter-wave optics becomes effectively nonlinear as soon as the atomic densities are high enough that collisions can no longer be ignored. The goal of this dissertation is to study selected aspects of atom optics under such conditions. Specifically, Chapter 2 studies the near-resonant dipole-dipole interaction between two atoms in tailored vacua. In contrast to spontaneous emission, whose rate is known to be influenced by the type of vacuum the atom interacts with, we find that the dipole-dipole potential is determined only by the free space vacuum and is not modified either by thermal or squeezed vacua. In addition in the far off-resonance regime we find that the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground state. In the second part of the dissertation, which comprises Chapter 3, we then study several aspects of the many-body theory of atomic ultracold systems in situations where the nonlinearity arises due to the two-body dipole-dipole interaction. After a formal theoretical development we discuss the possibility of using atomic phase conjugation off Bose condensates as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that phase conjugation provides an attractive alternative to the optical methods of probing condensate proposed in the past. We further study the elementary excitations in a multicomponent Bose condensates and determine the quasi-particle frequency spectrum. We show that in that case interferences resulting from cross-coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.

•Jan 1, 1996•0 citations

Cavity quantum electrodynamics with strong coupling in the optical domain

G. Rempe, R. J. Thompson, R. J. Brecha +1 more

The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.

Annual Meeting Optical Society of America•Jan 1, 1991•0 citations

Effects of dipole-dipole interaction on the transmitted spectrum of two-level atoms trapped in an optical cavity

Yuqing Zhang, Lei Tan, P. F. Barker

The transmission spectrum of two dipole-coupled atoms interacting with a single-mode optical cavity in the strong coupling regime is investigated theoretically for the lower and higher excitation cases. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom system. We find that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weakens them for the negative detuning cases for the lower excitation, which causes the spectrum to exhibit two asymmetric peaks with shifted heights and positions. For the higher excitation cases, the DDI augments the atomic saturation and leads to the deforming of the spectrum. Furthermore, the large DDI can cause the atom and the cavity to decouple, producing a singlet of the normal-mode spectrum.

arXiv:1207.2828•Physical Review A•Apr 23, 2014•30 citations

Nonperturbative atom-photon interactions in an optical cavity

H. J. Carmichael, L. Tian, Wei Ren

One of the principal developments in cavity quantum electrodynamics in the last few years has been the extension of the ideas originally applied to systems of Rydberg atoms in microwave cavities to optical frequencies. As a corollary of this, more attention is being paid to quantum fluctuations and photon statistics. Another development, still in its infancy, is a move toward experiments using slowed or trapped atoms, or velocity selected beams; these methods are needed to enter the nonperturbative (strong dipole coupling) regime for one atom where there are experiments on subtle quantum-statistical effects go carry out. In this chapter we solve a number of theoretical problems related to these themes. Although the focus of the work is on optical systems, most of what we do is also relevant at microwave frequencies. We emphasize quantum fluctuations and photon statistics, and we try always to separate the quantum physics from those aspects of the physics that are understandable in classical terms. On the whole we only pay attention to the nonperturbative regime of cavity quantum electrodynamics where the dipole coupling strength is larger than the dissipation rates. 59 refs., 14 figs.

•Dec 31, 1994•4 citations

Beyond the Rabi model: Light interactions with polar atomic systems in a cavity

Giovanni Scala, Karolina Słowik, Paolo Facchi A +2 more

The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.

arXiv:2103.11232•Physical Review A•Jul 27, 2021•14 citations
At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.
We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.
In contrast to electromagnetic fields, matter-wave fields are intrinsically interacting due to the presence of atom-atom collisions. Hence, matter-wave optics becomes effectively nonlinear as soon as the atomic densities are high enough that collisions can no longer be ignored. The goal of this dissertation is to study selected aspects of atom optics under such conditions. Specifically, Chapter 2 studies the near-resonant dipole-dipole interaction between two atoms in tailored vacua. In contrast to spontaneous emission, whose rate is known to be influenced by the type of vacuum the atom interacts with, we find that the dipole-dipole potential is determined only by the free space vacuum and is not modified either by thermal or squeezed vacua. In addition in the far off-resonance regime we find that the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground state. In the second part of the dissertation, which comprises Chapter 3, we then study several aspects of the many-body theory of atomic ultracold systems in situations where the nonlinearity arises due to the two-body dipole-dipole interaction. After a formal theoretical development we discuss the possibility of using atomic phase conjugation off Bose condensates as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that phase conjugation provides an attractive alternative to the optical methods of probing condensate proposed in the past. We further study the elementary excitations in a multicomponent Bose condensates and determine the quasi-particle frequency spectrum. We show that in that case interferences resulting from cross-coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.
The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.
The transmission spectrum of two dipole-coupled atoms interacting with a single-mode optical cavity in the strong coupling regime is investigated theoretically for the lower and higher excitation cases. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom system. We find that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weakens them for the negative detuning cases for the lower excitation, which causes the spectrum to exhibit two asymmetric peaks with shifted heights and positions. For the higher excitation cases, the DDI augments the atomic saturation and leads to the deforming of the spectrum. Furthermore, the large DDI can cause the atom and the cavity to decouple, producing a singlet of the normal-mode spectrum.
One of the principal developments in cavity quantum electrodynamics in the last few years has been the extension of the ideas originally applied to systems of Rydberg atoms in microwave cavities to optical frequencies. As a corollary of this, more attention is being paid to quantum fluctuations and photon statistics. Another development, still in its infancy, is a move toward experiments using slowed or trapped atoms, or velocity selected beams; these methods are needed to enter the nonperturbative (strong dipole coupling) regime for one atom where there are experiments on subtle quantum-statistical effects go carry out. In this chapter we solve a number of theoretical problems related to these themes. Although the focus of the work is on optical systems, most of what we do is also relevant at microwave frequencies. We emphasize quantum fluctuations and photon statistics, and we try always to separate the quantum physics from those aspects of the physics that are understandable in classical terms. On the whole we only pay attention to the nonperturbative regime of cavity quantum electrodynamics where the dipole coupling strength is larger than the dissipation rates. 59 refs., 14 figs.
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single-cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasiresonant with the cavity photon energy, and by neglecting the nonresonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one can derive the well-known phenomenology of quasiresonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments. Based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms, and parity-symmetry-breaking terms in order to identify the parameter regimes in which these different contributions play a significant role. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum.