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.

arXiv:1604.07883Physical Review LettersJul 28, 2016459 citations

Crossover polarons in a strongly interacting Fermi superfluid

Hui Hu, Jia Wang, Jing Zhou +1 more

We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid, by using a many-body $T$ -matrix approach that excludes Efimov trimer bound states. Termed the BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $\mathrm{\ensuremath{\Delta}}$, we find that the repulsive polaron branch becomes less well defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2\mathrm{\ensuremath{\Delta}}$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue, and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid, by using a many-body $T$-matrix approach that excludes Efimov trimer bound states. Termed the BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $\mathrm{\ensuremath{\Delta}}$, we find that the repulsive polaron branch becomes less well defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2\mathrm{\ensuremath{\Delta}}$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue, and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.

arXiv:2111.01372Physical Review AFeb 16, 202221 citations

Bose Polarons in the Strongly Interacting Regime

Ming-Guang Hu, Michael J. Van de Graaff, Dhruv Kedar +3 more

When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of ^{87}Rb with a much lower density gas of fermionic ^{40}K impurities. Through the use of a Feshbach resonance and radio-frequency spectroscopy, we characterize the energy, spectral width, and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, even as the two-body scattering length diverges.When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of ^{87}Rb with a much lower density gas of fermionic ^{40}K impurities. Through the use of a Feshbach resonance and radio-frequency spectroscopy, we characterize the energy, spectral width, and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, even as the two-body scattering length diverges.

arXiv:1605.00729Physical Review LettersJul 28, 2016442 citations

Phenomenological model of decaying Bose polarons

Ragheed Alhyder, Georg M. Bruun, Thomas Pohl +2 more

Cold atom experiments show that a mobile impurity particle immersed in a weakly interacting Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can, however, decay to lower energy states characterized by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the nonequilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.Cold atom experiments show that a mobile impurity particle immersed in a weakly interacting Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can, however, decay to lower energy states characterized by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the nonequilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.

arXiv:2507.04143Physical Review ResearchJan 15, 20260 citations

Bose Polarons at Finite Temperature and Strong Coupling

Nils-Eric Guenther, Pietro Massignan, Maciej Lewenstein +1 more

A mobile impurity coupled to a weakly interacting Bose gas, a Bose polaron, displays several interesting effects. While a single attractive quasiparticle is known to exist at zero temperature, we show here that the spectrum splits into two quasiparticles at finite temperatures for sufficiently strong impurity-boson interaction. The ground state quasiparticle has minimum energy at T_{c}, the critical temperature for Bose-Einstein condensation, and it becomes overdamped when T≫T_{c}. The quasiparticle with higher energy instead exists only below T_{c}, since it is a strong mixture of the impurity with thermally excited collective Bogoliubov modes. This phenomenology is not restricted to ultracold gases, but should occur whenever a mobile impurity is coupled to a medium featuring a gapless bosonic mode with a large population for finite temperature.A mobile impurity coupled to a weakly interacting Bose gas, a Bose polaron, displays several interesting effects. While a single attractive quasiparticle is known to exist at zero temperature, we show here that the spectrum splits into two quasiparticles at finite temperatures for sufficiently strong impurity-boson interaction. The ground state quasiparticle has minimum energy at T_{c}, the critical temperature for Bose-Einstein condensation, and it becomes overdamped when T≫T_{c}. The quasiparticle with higher energy instead exists only below T_{c}, since it is a strong mixture of the impurity with thermally excited collective Bogoliubov modes. This phenomenology is not restricted to ultracold gases, but should occur whenever a mobile impurity is coupled to a medium featuring a gapless bosonic mode with a large population for finite temperature.

arXiv:1708.08861Physical Review LettersFeb 1, 201893 citations

Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate

Arturo Camacho-Guardian, Georg M. Bruun

Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics.It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies.In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC).In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction.They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentumenergy between the quasiparticles is resonant with a sound mode in the BEC.We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results.Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas.The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC.Finally, we show how the Landau effective interaction leads to a sizable shift of the quasiparticle energy with an increasing impurity concentration, which should be detectable with presentday experimental techniques.Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics.It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies.In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC).In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction.They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentumenergy between the quasiparticles is resonant with a sound mode in the BEC.We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results.Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas.The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC.Finally, we show how the Landau effective interaction leads to a sizable shift of the quasiparticle energy with an increasing impurity concentration, which should be detectable with presentday experimental techniques.

arXiv:1712.06931Physical Review XAug 15, 201887 citations

T

-matrix approach that excludes Efimov trimer bound states. Termed the BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $\mathrm{\ensuremath{\Delta}}$, we find that the repulsive polaron branch becomes less well defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2\mathrm{\ensuremath{\Delta}}$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue, and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.