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arXiv:1401.0952 · Physical Review A

Radio-frequency spectroscopy of polarons in ultracold Bose gases

Aditya Shashi, Fabian Grusdt, Dmitry A. Abanin, Eugene Demler

Published May 16, 2014• 123 citations
arXivHTMLPDF

Abstract

Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a $\ensuremath{\delta}$-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.

DOI
10.1103/physreva.89.053617

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Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a \ensuremathδ\ensuremath{\delta}\ensuremathδ-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.
We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.
We discuss the interaction of a mobile quantum impurity with a Bose-Einstein condensate of atoms at finite temperature. To describe the resulting Bose polaron formation we develop a dynamical variational approach applicable to an initial thermal gas of Bogoliubov phonons. We study the polaron formation after switching on the interaction, e.g., by a radio-frequency (rf) pulse from a noninteracting to an interacting state. To treat also the strongly interacting regime, interaction terms beyond the Fröhlich model are taken into account. We calculate the real-time impurity Green's function and discuss its temperature dependence. Furthermore we determine the rf absorption spectrum and find good agreement with recent experimental observations. We predict temperature-induced shifts and a substantial broadening of spectral lines. The analysis of the real-time Green's function reveals a crossover to a linear temperature dependence of the thermal decay rate of Bose polarons as unitary interactions are approached.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate (BEC) of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. Already this highly simplified model allows insights into ultra-violet divergencies, logarithmic and power-law, that need to be properly regularized. To capture the physics near a Feshbach resonance, two-phonon scattering terms on the impurity as well as phonon-phonon interactions need to be included. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems, ranging from Lee-Low-Pines mean-field theory, Chevy-ansatz, Gross-Pitaevskii-equation to diagrammatic Monte Carlo approaches. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional 1D and 2D quantum systems; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics.However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized.Here, we use radio frequency spectroscopy of ultracold bosonic 39 K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC.We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity.The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states.Crucially, no significant effects of three-body decay are observed.Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ^{39}K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.