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arXiv:2104.11031

Synthetic gauge potentials for the dark state polaritons in atomic media

Yu-Hung Kuan, Siang-Wei Shao, I-Kang Liu, Julius Ruseckas, Gediminas Juzeliūnas, Yu‐Ju Lin, Wen-TeLiao

Published Apr 22, 2021• 0 citations
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Abstract

The quest of utilizing neutral particles to simulate the behaviour of charged particles in a magnetic field makes the generation of artificial magnetic field of great interest. The previous and the only proposal for the production of synthetic magnetic field for the dark state polaritons in electromagnetically induced transparency invokes the mechanical rotation of a sample. Here, we put forward an optical scheme to generate effective gauge potentials for stationary-light polaritons. 5To demonstrate the capabilities of our approach, we present recipes for having dark state polaritons in degenerate Landau levels and in driven quantum harmonic oscillator. Our scheme paves a novel way towards the investigation of the bosonic analogue of the fractional quantum Hall effect by electromagnetically induced transparency.

DOI
10.48550/arxiv.2104.11031

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In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman [3]. Although the first quantum computers of a few qubits have been realised experimentally [4, 5], the advent of scalable quantum computers might take another few decades. An alternative tool in the context of simulation is a highly controllable quantum system able to mimic the dynamics of other complex quantum systems, known as an analog quantum simulator. Cold neutral atoms and trapped ions have been shown to be versatile quantum simulators [6, 7] thanks to their high flexibility, controllability, and scalability. They permit one to study a wide range of problems arising from atomic physics, relativistic quantum physics, or cosmology [8]. Since neutral atoms do not carry any net charge, the simulation of electric and magnetic condensed matter phenomena, such as the spin Hall effect, seems out of reach. To overcome this apparent difficulty, the idea has been proposed to create artificial electromagnetic potentials for neutral atoms based on atom-light interaction [9– 12]. These artificial potentials act on neutral atoms as real electromagnetic potentials act on charged particles. Many works on artificial gauge potentials induced by atom-light interactions adopt a single-particle approach [12]. The predicted potentials are then supposed to be valid for a system of weakly interacting atoms. So far, the consequences of atom-atom interactions on the generation of artificial gauge fields has little been studied. The aim of this work is to study the artificial gauge fields arising from the interaction of two Rydberg atoms driven by a common laser field [13]. In this situation, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole [14] and van der Waals [15] interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [1] S. Lloyd, Science 273, 1073 (1996). [2] Yu. I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980. [3] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [4] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 460, 240 (2009). [5] N. Xu, J. Zhu, D. Lu, X. Zhou, X. Peng, and J. Du, Phys. Rev. Lett. 108, 130501 (2012). [6] I. Buluta and F. Nori, Science 326, 108 (2009). [7] I. Bloch, J. Dalibard and S. Nascimbéne, Nature Physics 8, 267 (2012). [8] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012). [9] G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). [10] G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). [11] G. Juzeliunas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006). [12] J. Dalibard, F. Gerbier, G. Juzeliu ̄nas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). [13] A. Cesa and J. Martin, Phys. Rev. A 88,062703 (2013). [14] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (2009). [15] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013).

•Jun 23, 2014•0 citations
The quest of utilizing neutral particles to simulate the behaviour of charged particles in a magnetic field makes the generation of artificial magnetic field of great interest. The previous and the only proposal for the production of synthetic magnetic field for the dark state polaritons in electromagnetically induced transparency invokes the mechanical rotation of a sample. Here, we put forward an optical scheme to generate effective gauge potentials for stationary-light polaritons. 5To demonstrate the capabilities of our approach, we present recipes for having dark state polaritons in degenerate Landau levels and in driven quantum harmonic oscillator. Our scheme paves a novel way towards the investigation of the bosonic analogue of the fractional quantum Hall effect by electromagnetically induced transparency.
We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-Lambda type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.
Ultracold gases are remarkably versatile and controllable systems with untapped potential to emulate a variety of quantum phenomena [1]. Atoms are, however, electrically neutral and therefore it is highly desirable to make them behave as charged particles. This capability has recently been demonstrated in a series of recent experiments [2–4]. Although many challenges remain ahead, atoms exposed to synthetic gauge field offer great opportunities for the realization of new classes of quantum materials with custom-designed properties, and with unforeseen applications. The first implementation of an effective magnetic field was accomplished by rotating an atomic cloud [5]. In the rotating frame of reference, an atom experiences the Coriolis force that emulates the Lorentz force experienced by a charged particle in a uniform magnetic field. Large vortex lattices have been created in this way, however, so far the strength of the effective magnetic field achieved by rotation is too weak to lead to new physics. An alternative approach invokes the vector potential, A, that induces a geometric phase as a charged particle moves around a closed loop. This notion of geometric phase can be adapted to a neutral atom that slowly moves in the presence of laser fields. If the lasers are chosen to ‘dress’ the internal atomic levels, so that the dressed eigenstates become position dependent, the center of mass adiabatically evolves according the operator p-A, instead of just p = −iℏ∇. The atom thus effectively moves as a charged particle in a magnetic field B = ∇ × A (see Fig. 1a). Exploiting this idea series of experiments have implemented artificial magnetic and electric fields [2–4]. The idea has also been implemented in the presence of a superimposed periodic optical lattice potential (see Fig. 1b). In this case, the length scale imposed by the lattice competes with the one associated with the magnetic field and can lead to frustration, manifested as an energy spectrum with fractal characteristics [2,3]. Light induced synthetic gauge fields: (a) A gas of neural atoms (green oval) can behave as a gas of charged particles when it is illuminated by a pair of laser beams (red arrows) that imparts momentum to the atoms and couples their internal (.|↑.〉, .|↓.〉) and motional degrees of freedom. The Raman beams that induce transitions between internal states also transfer two units of their linear momentum 2kL. This leads to the formation of dressed states (superpositions of states with different internal levels and center of mass momenta) which experience a modified kinetic energy, with an effective vector potential. If the effective vector potential has nonzero curl, the atoms move as charged particles in a magnetic field. (b) In the presence of an optical lattice potential, Raman beams can also induce an effective vector potential. In this case, the lattice is engineered so that along one direction atoms can tunnel between adjacent lattice sites (Jlight) only by absorbing and emitting photons from the beams. The imparted momentum from the lasers produces path-dependent phases that resemble the magnetic flux accumulated by a charged particle as it moves in a closed loop. The flux accumulated by the atoms when they move around a single unit cell, ϕ, can be significant (equivalent to the one generated by a real magnetic field of thousands tesla in an electronic system) and induce a fractal energy spectrum. Generalizations to emulate non-Abelian gauge potentials, associated in many cases to spin-orbit coupling can emerge when the geometric phase is replaced by a matrix acting on the internal Hilbert space [2–5]. This happens if there is a manifold of degenerate dressed states, such that even for arbitrarily slow motion, after traveling around a contour the particle ends up in a different internal state. Although various proposals for generating non-Abelian potentials exist, they remain to be implemented. On the other hand, Abelian spin-orbit coupling, arising from the momentum kicks imparted on the atom by the laser photons that drive internal transitions, has been realized in several laboratories using different laser configurations in alkali-metal (one outer electron) and alkaline-earth (two outer electrons) atoms [2–5]. There is a great vista ahead. For example, the inclusion of collisions or dipolar interactions will open a window to engineer fractional Hall liquids, unconventional superfluids and interacting topological phases. The creation of dynamical gauge fields important in many areas of physics such as quantum chromodynamics is also an open direction. The time is just ripe for investigating rich and unexplored physics with synthetic gauge fields for ultracold matter.
Abelian and non-Abelian gauge potentials and quantum gauge theories play central roles in our understanding of Nature. Gauge potentials are also of great significance in condensed matter physics. In fact, minimal coupling of electrons to an Abelian or non-Abelian gauge potential is the essential ingredient for the realization of topological states of matter. Due to the high controllability of ultracold atoms, they are commonly exploited to test fundamental theories of physics, simulate intractable systems, and realize exotic many-body states. Nonetheless, the charge neutrality of atoms places severe constraints on ultracold atomic systems, since neutral particles do not couple to gauge potentials the way charged particles do. That said, coupling a multi-component quantum gas to laser light can lead to the emergence of artificial Abelian and non-Abelian gauge potentials minimally coupled to the center-of-mass momenta of ultracold neutral atoms, paving the way for realizing topological states of matter and simulating gauge theories in quantum gases. All previous proposals for inducing gauge potentials have been developed in the semiclassical regime, where the radiation field is treated classically. I have developed a two-photon Raman scheme in the strong atom-photon coupling (i.e., quantum) regime, based on two counter-propagating modes of a ring cavity, to induce both synthetic magnetic field and spin-orbit coupling for a single neutral atom inside the cavity. The spin-orbit interaction is only weakly dependent on the occupation of the cavity modes, whereas the strength of the magnetic field is proportional to the square of the total number of photons in the cavity and can be made arbitrarily large, which is desirable for realizing the quantum Hall phase. I have then extended this single-atom cavity quantum-electrodynamics scheme to many bosons in the weak atom-photon coupling regime. In addition to inducing spin-orbit coupling for the individual atoms, the cavity fields also mediate infinite-ranged interactions between atoms, whose strengths and signs can readily be tuned experimentally. The interplay between these cavity-mediated interactions and the intrinsic two-body interactions determines the many-body ground state and its elementary excitations, with novel consequences such as the stabilization of an attractive Bose-Einstein condensate which otherwise is unstable.
The generation of a trapping potential for dark-state polaritons in a two-dimensional electromagnetically induced transparency system is theoretically studied. We show that such a trap can arise from a spatially inhomogeneous effective mass of the dark-state polariton. Because this mass inhomogeneity can be engineered by tuning the parameters of the control fields, the motion, spatial profile, and coherent behavior of bound dark-state polaritons can be tailored accordingly. Our results enable spatial controls of optical information and provide a possible route toward realizing Bose-Einstein condensation of dark-state polaritons in a trapping potential.
We study a washboard potential in a light-driven ensemble of three-level atoms induced by the externally applied magnetic fields under electromagnetically induced transparency (EIT). We find that a dark-state polariton, which is formed by an atomic ensemble dressed by the photon can display a typical quantum interference effect (i.e., the quasiparticle Bloch oscillation). The dark-state polariton is subjected to a washboard configuration potential with a spatially uniform force and a periodic potential provided by the linearly and periodically external magnetic fields, respectively. Due to the slower group velocity of the photons in the EIT medium, the period of Bloch oscillation can achieve a millisecond order of magnitude. Also, in our protocol, the Bloch oscillation of the dark-state polariton is feasibly modulated through the applied control and magnetic fields.
In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman [3]. Although the first quantum computers of a few qubits have been realised experimentally [4, 5], the advent of scalable quantum computers might take another few decades. An alternative tool in the context of simulation is a highly controllable quantum system able to mimic the dynamics of other complex quantum systems, known as an analog quantum simulator. Cold neutral atoms and trapped ions have been shown to be versatile quantum simulators [6, 7] thanks to their high flexibility, controllability, and scalability. They permit one to study a wide range of problems arising from atomic physics, relativistic quantum physics, or cosmology [8]. Since neutral atoms do not carry any net charge, the simulation of electric and magnetic condensed matter phenomena, such as the spin Hall effect, seems out of reach. To overcome this apparent difficulty, the idea has been proposed to create artificial electromagnetic potentials for neutral atoms based on atom-light interaction [9– 12]. These artificial potentials act on neutral atoms as real electromagnetic potentials act on charged particles. Many works on artificial gauge potentials induced by atom-light interactions adopt a single-particle approach [12]. The predicted potentials are then supposed to be valid for a system of weakly interacting atoms. So far, the consequences of atom-atom interactions on the generation of artificial gauge fields has little been studied. The aim of this work is to study the artificial gauge fields arising from the interaction of two Rydberg atoms driven by a common laser field [13]. In this situation, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole [14] and van der Waals [15] interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [1] S. Lloyd, Science 273, 1073 (1996). [2] Yu. I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980. [3] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [4] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 460, 240 (2009). [5] N. Xu, J. Zhu, D. Lu, X. Zhou, X. Peng, and J. Du, Phys. Rev. Lett. 108, 130501 (2012). [6] I. Buluta and F. Nori, Science 326, 108 (2009). [7] I. Bloch, J. Dalibard and S. Nascimbéne, Nature Physics 8, 267 (2012). [8] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012). [9] G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). [10] G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). [11] G. Juzeliunas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006). [12] J. Dalibard, F. Gerbier, G. Juzeliu ̄nas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). [13] A. Cesa and J. Martin, Phys. Rev. A 88,062703 (2013). [14] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (2009). [15] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013).