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arXiv:0909.3996 · Physical Review A

Supersymmetric response of a Bose-Fermi mixture to photoassociation

Tao Shi, Yue Yu, C. P. Sun

Published Jan 25, 2010• 21 citations
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Abstract

We study supersymmetric (SUSY) responses to a photoassociation (PA) process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon-induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle--$f$ hole pair continuum and the Nambu-Goldstone-fermion-like (or ``goldstino-like'') collective mode, are concomitant for a generic $b$-$f$ mixture, the former is completely suppressed in the SUSY $b$-$f$ mixture and the zero-momentum mode of the latter approaches an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, for example, the PA spectrum which displays the molecular formation rate of $\mathit{Ff}\ensuremath{\rightarrow}b$.

DOI
10.1103/physreva.81.011604

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We study supersymmetric (SUSY) responses to a photoassociation (PA) process in a mixture of Bose molecules bbb and Fermi atoms fff which turn to mutual superpartners for a set of proper parameters. We consider the molecule bbb to be a bound state of the atom fff and another Fermi atom FFF with different species. The bbb-fff mixture and a free FFF atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon-induced atom-molecule transition: While two new types of fermionic excitations, an individual bbb particle--fff hole pair continuum and the Nambu-Goldstone-fermion-like (or ``goldstino-like'') collective mode, are concomitant for a generic bbb-fff mixture, the former is completely suppressed in the SUSY bbb-fff mixture and the zero-momentum mode of the latter approaches an exact eigenstate. This SUSY response can be detected by means of the spectroscopy method, for example, the PA spectrum which displays the molecular formation rate of Ff\ensuremath→b\mathit{Ff}\ensuremath{\rightarrow}bFf\ensuremath→b.
We consider the process of photoassociation (PA) that occurs when a pair of colliding atoms interacts with a photon, thereby making a transition from the two-atom continuum to a bound molecular state. Such free-bound transitions are described by quantizing the molecule's dissociation continuum, and coupling each of these quasicontinuum (QC) levels to a similarly discrete molecular level. The correct free-atom results are recovered no later than at the end of a given calculation by taking the limit as the QC spacing tends to zero. From the quasicontinuum model, we are led to adapt the few-level and second-quantization methods of photon optics to analyze free-bound transitions. In particular, we establish the PA density parameter as nearly identical to the phase-space parameter as a Bose-Einstein condensate (BEC), illustrate the near-unit efficiency of one- and two-color photoassociation of a BEC, and develop coherent atom-molecule transitions as the matter optics version of second-harmonic generated photons. ^
Supersymmetry is assumed to be a basic symmetry of the world in many high-energy theories, but none of the superpartners of any known elementary particle have been observed yet. We argue that supersymmetry can also be realized and studied in ultracold atomic systems with a mixture of bosons and fermions, with properly tuned interactions and single particle dispersion. We further show that in such nonrelativistic systems supersymmetry is either spontaneously broken or explicitly broken by a chemical potential difference between the bosons and fermions. In both cases the system supports a sharp fermionic collective mode similar to the Goldstino mode in high-energy physics, due to supersymmetry. We also discuss possible ways to detect this mode experimentally.
We investigate nearly degenerate Bose-Fermi mixtures and show that the breaking of generalized supersymmetry (gSUSY) between bosons and fermions, with up to two internal states, manifests itself through the emergence of fermionic Goldstino modes with up to four flavors. In particular, we draw a distinction between typical supersymmetry (SUSY), where bosons have pseudospin 0 and fermions have pseudospin 1/2, and inverse supersymmetry (iSUSY), where bosons have pseudospin 1/2 and fermions have pseudospin 0. In such systems, we highlight that the Goldstino pseudospin is carried by either its constituent fermion (SUSY) or boson (iSUSY). We then distinguish between these two cases by depicting their differing effects on the spectral functions of the bosonic and fermionic atomic species. Lastly, we propose radio-frequency- or microwave-spectroscopy experiments, analogous to momentum (angular) resolved photoemission in condensed matter physics, to measure the pseudospin-dependent spectral functions and detect the emergence of Goldstino modes in mixtures of 39^{39}39K and 40^{40}40K.
We analyze the spectral properties of the Goldstino excitation in a Bose-Fermi mixture of cold atoms, whose masses and interaction strengths are tuned so that the Hamiltonian is supersymmetric. We consider systems at zero temperature and assume that, in the weak-coupling regime, the fermions form a Fermi sea, while the bosons form a Bose-Einstein condensate. We study the excitation spectrum within a simple extension of the random phase approximation, taking into account the mixing between the supercharge and the fermion caused by the condensate. This mixing affects the fermion spectrum strongly. We argue that the corresponding modification of the fermion spectrum, and the associated fermion distribution in momentum space, could be accessible experimentally and potentially allow for a determination of the Goldstino properties.
We theoretically investigate Raman photoassociation of a degenerate Bose-Fermi mixture of atoms and the subsequent prospect for anomalous (Cooper) pairing between atoms and molecules. Stable fermionic molecules are created via free-bound-bound stimulated Raman adiabatic passage which, in contrast to purely bosonic systems, can occur in spite of collisions. With the leftover atomic condensate to enhance intrafermion interactions, the superfluid transition to atom-molecule Cooper pairs occurs at a temperature that is roughly an order of magnitude below what is currently feasible.
We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.