Many-Body Effects in Rydberg Gases : Coherent Dynamics of Strongly Interacting Two-Level Atoms and Nonlinear Optical Response of a Rydberg Gas in EIT Configuration

Martin Gärttner

Jan 1, 20141 citation

Physical Review A

Many-body dynamics of Rydberg excitation using the Ω expansion

Jovica Stanojevic, Robin Côté

Published May 12, 2010• 9 citations

Publisher

Abstract

\ensuremath{\Omega}

. In the Heisenberg picture, we give recurrence relations to calculate any order of these expansions, which are expected to be well behaved for arbitrarily strong interactions. For large homogeneous samples, the explicit terms of the expansions, up to

{\ensuremath{\Omega}}^{4}

, are given and then averaged over all possible random spatial distributions of atoms for the most important cases of excitation pulses and interactions.

DOI: 10.1103/physreva.81.053406

Related papers

Many-body dynamics of Rydberg excitation using the $Ω$ -expansion

Jovica Stanojevic, Robin Côté

We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $Ω$ . In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $Ω^4$ , averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $Ω$. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $Ω^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.

arXiv:0801.2396Jan 15, 20080 citations

Effects of strong interactions in ultracold Rydberg gases

Jovica Stanojevic

In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^

Jan 1, 20071 citation

Many-body Rabi oscillations of Rydberg excitation in small mesoscopic samples

Jovica Stanojevic, Robin Côté

We investigate collective aspects of Rydberg excitations in ultracold mesoscopic samples. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitations are many-body Rabi oscillations, spatial correlations between atoms, as well as fluctuations in the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\"odinger equation, using a ``superatom'' approach. We find that, under certain conditions, these many-body behaviors could be observed experimentally.We investigate collective aspects of Rydberg excitations in ultracold mesoscopic samples. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitations are many-body Rabi oscillations, spatial correlations between atoms, as well as fluctuations in the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\"odinger equation, using a ``superatom'' approach. We find that, under certain conditions, these many-body behaviors could be observed experimentally.

arXiv:0801.2406Physical Review ASep 28, 200944 citations

Correlations of Rydberg excitations in an ultracold gas after an echo sequence

Sebastian Wüster, Jovica Stanojevic, Cenap Ates +4 more

We show that Rydberg states in an ultracold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100, 013002 (2008)]. Near the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius halfway through the pulse. These correlations lead to large deviations of the atom-counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. Finally, we demonstrate the utility of the $\ensuremath{\omega}$ expansion for the approximate description of correlation dynamics through an echo sequence.We show that Rydberg states in an ultracold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100, 013002 (2008)]. Near the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius halfway through the pulse. These correlations lead to large deviations of the atom-counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. Finally, we demonstrate the utility of the $\ensuremath{\omega}$ expansion for the approximate description of correlation dynamics through an echo sequence.

arXiv:0911.0772Physical Review AFeb 8, 201021 citations

Strong Spin-Motion Coupling in the Ultrafast Dynamics of Rydberg Atoms

Vineet Bharti, Seiji Sugawa, Masaya Kunimi +7 more

Rydberg atoms in optical lattices and tweezers is now a well-established platform for simulating quantum spin systems. However, the role of the atoms' spatial wave function has not been examined in detail experimentally. Here, we show a strong spin-motion coupling emerging from the large variation of the interaction potential over the wave function spread. We observe its clear signature on the ultrafast many-body nanosecond-dynamics of atoms excited to a Rydberg S state, using picosecond pulses, from an unity-filling atomic Mott-insulator. We also propose an approach to tune arbitrarily the strength of the spin-motion coupling relative to the motional energy scale set by trapping potentials. Our work provides a new direction for exploring the dynamics of strongly correlated quantum systems by adding the motional degree of freedom to the Rydberg simulation toolbox.Rydberg atoms in optical lattices and tweezers is now a well-established platform for simulating quantum spin systems. However, the role of the atoms' spatial wave function has not been examined in detail experimentally. Here, we show a strong spin-motion coupling emerging from the large variation of the interaction potential over the wave function spread. We observe its clear signature on the ultrafast many-body nanosecond-dynamics of atoms excited to a Rydberg S state, using picosecond pulses, from an unity-filling atomic Mott-insulator. We also propose an approach to tune arbitrarily the strength of the spin-motion coupling relative to the motional energy scale set by trapping potentials. Our work provides a new direction for exploring the dynamics of strongly correlated quantum systems by adding the motional degree of freedom to the Rydberg simulation toolbox.

arXiv:2311.15575Physical Review LettersAug 30, 202415 citations

Many-Body Effects in Rydberg Gases : Coherent Dynamics of Strongly Interacting Two-Level Atoms and Nonlinear Optical Response of a Rydberg Gas in EIT Configuration

Martin Gärttner

Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.

Jan 1, 20141 citation

\ensuremath{\Omega}

{\ensuremath{\Omega}}^{4}

, are given and then averaged over all possible random spatial distributions of atoms for the most important cases of excitation pulses and interactions.

Ω

. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to

Ω^4

, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.