Geometric squeezing into the lowest Landau level

Fletcher, R.; Shaffer, Airlia; Wilson, Cedric; Patel, Parth; Yan, Zhenjie; Crépel, Valentin; Mukherjee, Biswaroop; Zwierlein, Martin

doi:10.1126/science.aba7202

Cited by 46 publications

(43 citation statements)

References 55 publications

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“…In particular, E f /E i = (1 + s −1 Υ)/2 when Ω f → 0. The same result can be obtained directly from Formulas (165)-(167), if one uses solution (45) (with Ω instead of ω) and its consequencies:…”

Section: Non-adiabatic Evolutionmentioning

confidence: 67%

“…Consequently, the adiabatic regime corresponds to values u 1, whereas the case of u 1 can be considered as a smooth analog of sudden jump. Note that function ( 75) is close to (45) for τ 1 and u 1. However, these functions do not coincide exactly.…”

Section: Inverse Linear Decrease Of Magnetic Fieldmentioning

confidence: 77%

“…Operators (4) describe nothing but the coordinates of the center of a circle, which the particle rotates around with the cyclotron frequency Ω = eB/(mc). The importance of these integrals of motion was emphasized by many authors during decades [4,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Equivalent integrals of motion, obtained by the multiplication of x c and y c by mΩ, were considered under the name "pseudomomentum" in papers [36,46].…”

Section: Main Physical Quantitiesmentioning

confidence: 99%

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Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Dodonov

Horovits

2021

Entropy

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We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

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Section: Non-adiabatic Evolutionmentioning

confidence: 67%

Section: Inverse Linear Decrease Of Magnetic Fieldmentioning

confidence: 77%

Section: Main Physical Quantitiesmentioning

confidence: 99%

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Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Dodonov

Horovits

2021

Entropy

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“…The most exciting possibility is realizing fractional quantum Hall physics and observing non-abelian phases of matter [1]. A recent experiment at MIT [2] made an important step towards achieving this goal. They found that when rotating a Bose gas in an anisotropic trap, the resulting nonequilibrium dynamics can drive the atoms into the lowest Landau level, a pre-requisite for observing the quantum Hall effect.…”

Section: Introductionmentioning

confidence: 99%

Rotating Bose gas dynamically entering the lowest Landau level

Sharma,

Mueller

2021

Preprint

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“…Early cold atom experiments used rotating traps to mimic the effect of the external magnetic field needed to reach the FQH regime [19][20][21]. In this setup, first signatures of the bosonic Laughlin state at ν = 1 2 have been observed [22].…”

mentioning

confidence: 99%

Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge

Palm¹,

Mardazad²,

Bohrdt³

et al. 2021

Preprint

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Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and characterization of such states, where novel detection schemes enable an unprecedented microscopic understanding. Here we show that the central charge can be directly measured in current cold atom experiments using the number entropy as a proxy for the entanglement entropy. We perform density-matrix renormalization-group simulations of Hubbardinteracting bosons on coupled chains subject to a magnetic field with α = 1 /4 flux quanta per plaquette. Tuning the inter-chain hopping, we find a transition from a trivial quasi-one dimensional phase to the topologically ordered Laughlin state at magnetic filling factor ν = 1 /2 for systems of three or more chains. We resolve the transition using the central charge, on-site correlations, momentum distributions and the many-body Chern number. Additionally, we propose a scheme to experimentally estimate the central charge from Fock basis snapshots. The model studied here is experimentally realizable with existing cold atom techniques and the proposed observables pave the way for the detection and classification of a larger class of interacting topological states of matter.

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Geometric squeezing into the lowest Landau level

Cited by 46 publications

References 55 publications

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Rotating Bose gas dynamically entering the lowest Landau level

Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge

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