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Observation of a Smooth Polaron–Molecule Transition in a Degenerate Fermi Gas

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Observation of a Smooth Polaron–Molecule Transition in a Degenerate Fermi Gas Observation of a smooth polaron{molecule transition in a degenerate Fermi gas Gal Ness,1 Constantine Shkedrov,1 Yanay Florshaim,1 2, 3 2, 3 2, 3 1, Oriana K. Diessel, Jonas von Milczewski, Richard Schmidt, and Yoav Sagi ∗ 1Physics Department, Technion { Israel Institute of Technology, Haifa 32000, Israel 2Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Strasse. 1, 85748 Garching, Germany 3Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 M¨unchen,Germany (Dated: September 29, 2020) Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing chal- lenge in many-body physics. When the interactions are short-ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoret- ically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact pa- rameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition. Our findings establish Raman spectroscopy as a powerful ex- perimental tool for probing the physics of mobile quantum impurities and shed new light on the competition between emerging fermionic and bosonic quasiparticles in non-Fermi-liquid phases. I. INTRODUCTION complete loss of quasiparticle behavior [18]. In contrast, for mobile impurities, the energy cost related to the im- In order to understand the motion of an electron purity recoil stabilizes the formation of Fermi polarons through an ionic lattice, Landau suggested treating the with well-defined quasiparticle properties [19]. electron and the phonons that accompany its movement One of the simplest scenarios in which Fermi polarons as a new quasiparticle named `polaron' [1]. The con- naturally emerge is in ultracold gases, where a small num- cept of the polaron was later found to be applicable in ber of (mobile) spin impurities can be immersed in a sys- many other systems, including semiconductors [2], high- tem of free fermions of the opposite spin. Such ultracold, temperature superconductors [3], alkali halide insulators spin-imbalanced systems are ideally suited to explore po- [4], and transition metal oxides [5]. In such systems, po- laron physics [14, 20, 21] owing to their extremely long larons appear as weakly- or strongly-coupled quasiparti- spin-relaxation times and tunability of the s-wave scat- cles that are classified as large or small, depending on tering length, a, between the impurity and the majority the size of the distortion they generate in the underlying atoms via Feshbach resonances [22]. crystalline structure of the material [6]. Understanding the properties of polarons coupled to a bosonic bath is Initial experiments with spin-imbalanced Fermi gases still an ongoing effort in areas ranging from solid-state in harmonic confinement revealed phase separation into three regions at unitary interactions (a ). It was physics [7, 8] and ultracold atoms [9{11], to quantum ! 1 chemistry [12]. observed that phases arrange according to the varying The concept of polarons becomes also a powerful tool local density, with an inner core of a spin-balanced su- for our understanding of the properties of quantum im- perfluid being separated from a second shell of a partially purities interacting with a fermionic environment. In this polarized normal gas, and a third shell of a fully polar- 3 ized gas [23{25]. It was Chevy who first pointed out arXiv:2001.10450v3 [cond-mat.quant-gas] 27 Sep 2020 context, applications range from ions in liquid He [13], and mixtures of cold atomic gases [14] to excitons in- [26] that the radius between the outer and intermediate teracting with electrons in atomically thin semiconduc- shells is related to the solution of the Fermi polaron prob- tors [15{17]. Strikingly, in fermionic systems an infinite lem [27]. For weak attractive interactions (a < 0), the number of low-energy excitations leads to the Anderson ground state is a long-lived quasiparticle dressed by the orthogonality catastrophe for immobile impurities and a majority particles, forming the attractive polaron. Be- yond the Feshbach resonance, at a > 0, it was found that a metastable polaronic state also exists energetically far up in the excitation spectrum [28{35]. This so-called re- ∗ Electronic address: [email protected] pulsive polaron becomes, however, progressively unstable 2 towards unitary interactions. is still open. Fermi polarons have well-defined momenta with a nar- In this work, we address this question both theoret- row dispersion relation that is described by a renormal- ically and experimentally. Our experiments are per- ized effective mass [29, 36]. The attractive polaron per- formed with a spin-imbalanced, ultracold Fermi gas in sists as the ground state even as the interactions increase the BEC-BCS crossover regime [22, 46]. To gain detailed towards unitarity. However, for still stronger interac- insight into the behavior of the quasiparticles, we employ tions, the system favors a molecular ground state dressed a novel spectroscopic method based on a two-photon Ra- by the majority fermions [27, 37, 38] (see Fig. 3(a) be- man transition. Raman spectroscopy allows us to clearly low). It was predicted that the energies of the polaron identify the coherent response of the polarons, and deter- 1 and molecular states cross around (k a)− 0:9 |with mine some of its key properties, including its energy and F c ≈ kF being the Fermi wave vector of the majority| leading spectral weight. We compare our results with a theoret- to a sharp, first-order transition between the two ground ical model that takes into account the thermal occupa- states [27, 29, 37{40]. Contrasting claims for a smooth tion of polarons and molecules at finite momenta. Both crossover were also put forward [41{44]. our theoretical model and the measurements consistently The Fermi polaron problem represents the limiting show that a finite impurity concentration and tempera- case of a spin-imbalanced Fermi gas. Therefore, the na- ture have a striking effect on the transition: they smooth ture of the polaron-to-molecule transition has profound it and lead to a regime where polarons and molecules theoretical implications for the phase diagram of the coexist. spin-imbalanced BEC-BCS crossover [38, 45{48]. While After describing the experimental setup in Section II, at zero temperature, the polaron-to-molecule transition we briefly introduce our theoretical model in Section III was predicted to be pre-empted by phase separation be- and present the calculated Raman spectra. Based on tween the superfluid and the normal phases [49], at finite this, in Section IV we develop a fitting routine for the temperature, increased thermal fluctuations are expected experimental spectra which allows us to extract physical to suppress the superfluid and restore the polaron-to- quantities, such as the polaron energy, the quasiparticle molecule transition. Experimentally, the Fermi polaron spectral weight, and the contact parameter. The experi- was initially studied by radio-frequency (rf) spectroscopy, mental results are presented and discussed in Section V, where the attractive polaron was identified by a narrow while in Section VI we give a detailed theoretical deriva- peak appearing exclusively in the minority spectrum [50]. tion of our model. In particular, we show how the quanti- The spectral weight of this peak was interpreted as the ties accessible in the experiment are computed. Finally, quasiparticle residue (or weight) Z, which quantifies how in Section VII, we summarize our results, discuss their similar the polaron remains to the non-interacting impu- implications for the many-body physics of cold Fermi rity particle. Accordingly, it is determined by the overlap gases and outline directions for future work. between the polaron wavefunction and its non-interacting impurity state. When Z is zero, the quasiparticle descrip- tion is no longer valid. In the experiment, Z was observed II. THE EXPERIMENTS to continuously decrease and vanish above a certain in- teraction strength in contrast to theoretical predictions The experiments are performed with a harmonically- based on the Chevy Ansatz wavefunction [38]. trapped ultracold gas of 40K atoms. The system is ini- A different approach to measure Z was employed in tially prepared in an incoherent mixture of the two low- Ref. [31]. Here, Z was determined from coherent oscilla- est Zeeman states denoted by 1 and 2 (see Fig. 1), tions between the polaron and a non-interacting impurity with the majority of atoms beingj i in statej i1 . The cool- state. In this approach, the coherent oscillations address ing sequence is similar to the one describedj i in Ref. [56], the polaronic state even when the attractive polaron is here modified to produce a spin-polarized ensemble of an excited state above the molecular ground state.
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