Topological Growing of Laughlin States in Synthetic Gauge Fields

Abstract

We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions (CF) along with magnetic flux quanta one-by-one. The topologically protected Thouless pump ("Laughlin's argument") is used to create two localized flux quanta and the resulting hole excitation is subsequently filled by a single boson, which, together with one of the flux quanta forms a CF. Using our protocol, filling 1/2 LN states can be grown with particle number N increasing linearly in time and strongly suppressed number fluctuations. To demonstrate the feasibility of our scheme, we consider two-dimensional (2D) lattices subject to effective magnetic fields and strong on-site interactions. We present numerical simulations of small lattice systems and discuss also the influence of losses. Introduction In recent years topological states of matter [1][2][3][4][5][6][7][8] have attracted a great deal of interest, partly due to their astonishing physical properties (like fractional charge and statistics) but also because of their potential practical relevance for quantum computation [9,10]. While these exotic phases of matter were first explored in the context of the quantum Hall effect of electrons subject to strong magnetic fields [11,12], there has been considerable progress recently towards their realization in cold-atom [13][14][15][16] as well as photonic [17][18][19][20][21][22][23] systems. A particularly attractive feature of such quantum Hall simulators are the comparatively large intrinsic length scales which allow coherent preparation, manipulation and spatially resolved detection of exotic many-body phases and their excitations.

Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity

“…However, the efficiency of this approach is expected to quickly decrease for larger photon numbers as they employ multi-photon transitions with low probabilities and generally lead to a superposition of states with different particle numbers. Recently, new strategies have been put forward to remedy these unwanted properties of coherent pumping, including a flux insertion technique supplemented again by a coherent drive [14].…”

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

“…Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed. …”

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

“…In this context, several theoretical studies investigated the adiabatic preparation of different FCI states and the associated phase diagrams [35][36][37][38][39][40]. Some works focused on the numerical characterization of these states by inspecting key quantities such as the many-body Chern number, the particle entanglement spectrum, the behavior of the correlation functions and the topological entanglement entropy [41][42][43], while others proposed ex-perimentally applicable schemes to identify these elusive strongly correlated phases of matter [44,45].…”