Superradiant Topological Peierls Insulator inside an Optical Cavity
Farokh Mivehvar · Helmut Ritsch · Francesco Piazza
Abstract and summary · read the original at the source
In one page
Put a cloud of ultracold atoms inside a mirrored box — an optical cavity — and shine a laser across it. Above a certain brightness the atoms stop sitting evenly and snap into a regular pattern of their own making, because that pattern scatters the laser light into the cavity most efficiently. Farokh Mivehvar, Helmut Ritsch and Francesco Piazza show that when the laser is tuned to the blue side of the atomic transition, the crystal the atoms build for themselves comes in two mirror-image versions, and which one the cloud happens to pick decides what kind of material it becomes: an ordinary insulator, or a topological one carrying a protected pair of states at its ends. The cavity light does the job that the vibrations of a real crystal do in a solid — it opens an energy gap. And the answer can be read off the light leaking out of the cavity without touching the atoms at all. It is a laboratory in which a light field designs matter.
Why it matters hereChapter 2’s newest result is the dark-cavity superconductor: reshape the vacuum’s own spectrum with a cavity and matter changes state. This paper is the same programme in full view — the cavity field and the atoms design each other, and the phase they settle into can be read straight off the emitted light. Chapter 11 asks how far coherent quantum matter can be steered by a field, and this is a worked example with the measurement already specified.
What it claims
01The known superradiant self-ordering transition also occurs for low-field-seeking fermionic particles, when the pump laser is tuned to the blue side of the atomic transition: above a threshold pump intensity the homogeneous gas density spontaneously breaks a Z2 symmetry into a spatially periodic order, which collectively scatters pump photons into the cavity.Abstract; the Emergent dimerized superradiant lattice section and Figure 2
Published and peer-reviewed02The optical lattice that emerges from the interference of pump and cavity light is homopolar — two sites per unit cell with no energy offset between them — and has two distinct dimerizations, chosen spontaneously. The Zak phase of the lowest Bloch band, the Berry phase picked up crossing the whole Brillouin zone, is quantised by chiral symmetry to either zero or pi, and the non-zero value marks a topologically non-trivial band.Introduction, the homopolar-versus-heteropolar paragraph; the superradiant lattice potential, Equation 3; the Zak phase, Equation 5
Published and peer-reviewed03When the Fermi momentum sits close to half the cavity-mode wavenumber, a Peierls-like instability opens a gap at the Fermi surface — the same mechanism as in electron-phonon models, except that a single global cavity photon mode plays the part of the many phonon modes. For the pi dimerization the result is a superradiant topological insulator with chiral symmetry, in the AIII class and, in the tight-binding limit, the BDI class of the Su-Schrieffer-Heeger model, hosting a pair of localised edge states in the gap of a finite system.Introduction, the Peierls-instability paragraph; Topological insulator section; phase diagram Figure 3; edge-state spectrum in the inset of Figure 4 for a 50-unit-cell lattice
Published and peer-reviewed04The topology can be read out non-destructively and in real time from the cavity output: the bulk Zak phase coincides with the relative phase between pump laser and cavity field, and the edge states open an extra absorption channel in a well-defined frequency window running from half the gap to half the gap plus the conduction bandwidth, appearing as additional broadening of the cavity resonance in the fluorescence or probe-transmission spectrum.Abstract, final sentence; Detecting edge states section, the polarizability of Equation 6 and Figure 4
Published and peer-reviewed05The configuration needs no artificial spin-orbit coupling and no synthetic gauge field: the authors state that it is already experimentally available in the existing superradiant self-ordering apparatus by a simple change of the trapping laser frequency towards blue atom-pump detuning.Introduction, the paragraph introducing the Letter; Conclusions
Designed, not yet built06Above a second and stronger pump threshold the self-ordered phase loses stability — the self-consistent equations have no stable solution — because of the competition between the cosine and cosine-squared contributions to the superradiant lattice potential, which is characteristic of the blue-detuned homopolar lattice and can mark the onset of limit-cycle and even chaotic behaviour.Topological insulator section, closing paragraph; the grey-shaded regions of Figures 2 and 3
What to watch
Read it · abstract
Abstract
We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity the homogeneous gas density breaks a Z2 symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue-detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization the resulting Bloch bands can have a non-trivial topological structure characterized by a non-vanishing Zak phase. In the case the Fermi momentum is close to half the cavity-mode wavenumber, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be non-destructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well defined frequency window of the cavity spectrum.
F. Mivehvar, H. Ritsch and F. Piazza, Institut für Theoretische Physik, Universität Innsbruck. Physical Review Letters 118, 073602 (2017); preprint arXiv:1611.04876.
(Abstract only. The complete Letter — the model Hamiltonian and self-consistent mean-field equations, the phase diagram in pump strength against Fermi momentum, the edge-state spectrum of the finite lattice and the cavity absorption calculation — is at the source; see the rights note above for why the full text is not reproduced here.)
The way in
https://doi.org/10.1103/PhysRevLett.118.073602Published as Physical Review Letters 118, 073602 (2017) under the APS default licence, and posted to arXiv as 1611.04876 under the arXiv non-exclusive distribution licence 1.0 — neither is an open licence and no Creative Commons statement appears in the text or on the arXiv record, so this page carries the summary, the claims and the authors’ own abstract and sends the reader to the source. The abstract below is transcribed from the arXiv preprint, with the preprint’s spelling of ’topological’ restored.
How to cite it
Farokh Mivehvar, Helmut Ritsch, Francesco Piazza (2017) Superradiant Topological Peierls Insulator inside an Optical Cavity. doi:10.1103/PhysRevLett.118.073602
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