Ultracold Superstrings in Atomic Boson-Fermion Mixtures

Abstract

We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry. DOI: 10.1103/PhysRevLett.95.250401 PACS numbers: 03.75.Mn, 11.25.ÿw, 32.80.Pj, 67.40.ÿw In recent years, three topics have, in particular, attracted a lot of attention in the area of ultracold atomic gases. These topics are vortices [1][2][3][4][5], boson-fermion mixtures [6 -10], and optical lattices [11,12]. In this Letter we propose to combine these three topics to engineer a superstring in the laboratory, i.e., a linelike quantum object with both bosonic and fermionic excitations and a supersymmetric Hamiltonian that is invariant under interchanges of these excitations. The physics of a vortex line in a onedimensional optical lattice has been studied recently [13,14]. Because of the optical lattice, the transverse quantum fluctuations of the vortex line are greatly enhanced in this configuration. The vortex can therefore be viewed as a quantum mechanical string and it forms the bosonic part of our superstring. In addition, we propose to trap fermionic atoms in the vortex core, to make a nonrelativistic version of a so-called Green-Schwarz superstring in four spacetime dimensions. Because our ultracold superstring is nonrelativistic, it is not constrained to the ten-dimensional spacetimes in which superstrings are usually studied in highenergy physics. The precise mathematical connection with string theory is currently under investigation.Apart from the connection to string theory, our ultracold superstring is also of interest in its own right. To the best of our knowledge, it is the first condensed-matter system proposed where supersymmetry can be studied experimentally. The intriguing possibility of observing effects of supersymmetry is common in high-energy physics, but novel in a condensed-matter setting. In this particular case, the supersymmetry protects the superstring from spiraling out of the gas. This can be understood from the fact that the dissipation resulting in this motion has two sources, namely, the creation of two additional bosons in the transverse oscillations of the vortex, and the production of an additional particle-hole pair of fermions. At the supersymmetric point these two contributions interfere destructively and the stability of the superstring is greatly enhanced. Moreover, the ultracold superstring allows for the study of a quantum phase transition that spontaneously breaks supersymmetry. Experimentally this will be directly visible by observing the superstring spiraling out of the center of the gas. Note that supersymmetry can only be real...

One-Loop Renormalization Group Analysis of Bose–fermi Mixtures

“…It has been one of the most active research areas in the high energy physics [30]. Various researches were also conducted to find supersymmetry in condensed matter systems [7,8]. …”

“…Various theoretical researches have been proposed. For instance, formation of stable strongly correlated boson-fermion pairs [2], instability of the mixture when there is an attraction between bosons and fermions [3,4], interspecies interactions induced attraction among bosons [5,6] and emergent supersymmetry (SUSY) from mixtures of cold Bose and Fermi atoms [7,8]. Recent developments in atomic experiments have made it possible to realize boson-fermion mixed gases in the laboratory.…”

Quantum degenerate Bose-Fermi mixtures on one-dimensional optical lattices

“…In addition to "conventional" systems such as He 3 -He 4 mixtures or systems with strong electron-phonon coupling, degenerate boson-fermion mixtures have recently been realized with ultracold atomic gases in optical traps. Stable boson-fermion mixtures have been realized with 6 Li- 7 Li, 1 23 Na- 6 Li, 2 87 Rb-40 K, 3 and 6 Li-87 Rb. 4 These experiments with ultracold atoms give the ability to create perfectly clean and defect free samples and unprecedented control over the interaction parameters-in short, an ideal testbed for studying many-body phenomena.…”

“…In this limit, the Hamiltonian ͑1͒ is identical to that recently proposed for ultracold superstrings in Bose-Fermi mixtures. 7 An insight into the model ͑1͒ can be gained by studying the limiting cases. For V = 0, the boson and fermion sectors are decoupled.…”

“…[5][6][7][8][9][10][11] For the mixture of bosons and spin-polarized fermions on the lattice, ground state phases include two component mixtures, pure bosonic and fermionic domains, and a novel mixed phase with a charge gap but with a gapless mode of mixture composition fluctuations. In an actual setup of optical trap experiments, domains of several phases may be simultaneously manifested depending on the local trap potential.…”