arXiv subjects

R. Côté

Publications and source records attributed to R. Côté.

At least 19 recordsLinked to original sources

arXiv2025

Quantum correction to the Langevin cross section in resonant-exchange processes

Resonant-exchange scattering plays a key role in many-body dynamics and transport phenomena (such as spin, charge, or excitation diffusion) at low and moderate temperatures. Recent investigations have shown that the locking of phase shifts is central to resonant-exchange scattering at low energies. Moreover, phase-shift locking causes an unexpected behavior, namely the resonant-exchange cross section over a broad range of energies is largely dictated by $s$-wave scattering, whose influence extends high above the $s$-wave Wigner regime. Here, we generalize our previous treatment to higher energies and derive an analytical expression for the resonant-exchange cross section which depends on a few parameters and accounts not only for the locking of phase shifts, but also for their gradual unlocking with increased energy. We find good agreement between the computed (fully quantal) cross sections and those obtained with our expression, which we illustrate in great detail for the case of resonant charge-transfer in ion-atom collisions.

quant-ph↗

arXiv2019

Phase-amplitude formalism for ultra-narrow shape resonances

We apply Milne's phase-amplitude representation [W. E. Milne, Phys. Rev. 35, 863 (1930)] to a scattering problem involving disjoint classically allowed regions separated by a barrier. Specifically, we develop a formalism employing different sets of amplitude and phase functions --- each set of solutions optimized for a separate region --- and we use these locally adapted solutions to obtain the true value of the scattering phase shift and accurate tunneling rates for ultra-narrow shape resonances. We show results for an illustrative example of an attractive potential with a large centrifugal barrier.

physics.atom-ph↗

arXiv2017

Integral representation for scattering phase shifts via the phase-amplitude approach

A novel integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys. Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential equation for the amplitude function $y$ with an equivalent linear equation for the envelope $ρ=y^2$, which renders the integral representations highly amenable to numerical implementations. The phase shift is obtained directly from Milne's phase function, which in turn is expressed in terms of the envelope function. The integral representation presented in this work is fully general and it can be used for any type of scattering potential, including the Coulomb potential.

physics.atom-ph↗

arXiv2017

Editorial: Special Issue on the Atomic and Molecular Processes in the Ultracold Regime, the Chemical Regime, and Astrophysics

This editorial introduces the J. Phys. B: Atomic, Molecular and Optical Physics Special Issue "Atomic and Molecular Processes in the Ultracold Regime, the Chemical Regime and Astrophysics" dedicated to Professor Alexander Dalgarno (1928-2015). After a brief biographical review, short summaries of the contributed papers and their relations to some of Prof. Dalgarno's work are given.

physics.hist-ph↗

arXiv2017

Nuclear magnetic resonance line shapes of Wigner crystals in $^{13}$C-enriched graphene

Assuming that the nuclear magnetic resonance (NMR) signal from a $^{13}$C isotope enriched layer of graphene can be made sufficiently intense to be measured, we compute the NMR\ lineshape of the different crystals ground states that are expected to occur in graphene in a strong magnetic field. We first show that in nonuniform states, there is, in addition to the frequency shift due to the spin hyperfine interaction, a second contribution of equal importance from the coupling between the orbital motion of the electrons and the nuclei. We then show that, if the linewidth of the bare signal can be made sufficiently small, the Wigner and bubble crystals have line shapes that differ qualitatively from that of the uniform state at the same density while crystal states that have spin or valley pseudospin textures do not. Finally, we find that a relatively small value of the bare linewidth is sufficient to wash out the distinctive signature of the crystal states in the NMR line shape.

cond-mat.mes-hall↗

arXiv2017

Molecular Hydrogen: a benchmark system for Near Threshold Resonances at higher partial waves

Benchmark reactions involving molecular hydrogen, such as H$_2$+D or H$_2$+Cl, provide the ideal platforms to investigate the effect of Near Threshold Resonances (NTR) on scattering processes. Due to the small reduced mass of those systems, shape resonances due to particular partial waves can provide features at scattering energies up to a few Kelvins, reachable in recent experiments. We explore the effect of NTRs on elastic and inelastic scattering for higher partial waves $\ell$ in the case of H$_2$+Cl for $s$-wave and H$_2$+D for $p$-wave scattering, and find that NTRs lead to a different energy scaling of the cross sections as compared to the well known Wigner threshold regime. We give a theoretical analysis based on Jost functions for short range interaction potentials. To explore higher partial waves, we adopt a three channel model that incorporates all key ingredients, and explore how the NTR scaling is affected by $\ell$. A short discussion on the effect of the long-range form of the interaction potential is also provided.

physics.atom-ph↗

arXiv2016

Resonances at very low temperature for the reaction D$_2$+H

We present numerical results for rate coefficients of reaction and vibrational quenching in the collision of H with D$_2(v,j)$ at cold and ultracold temperatures. We explore both ortho-D$_2(j\!=\!0)$ and para-D$_2(j\!=\!1)$ for several initial vibrational states $(v\leq 5)$, and find resonant structures in the energy range 0.01--10 kelvin, which are sensitive to the initial rovibrational state $(v,j)$. We compare the reaction rates for D$_2$+H with our previously obtained results for the isotopologue reaction H$_2$+D, and discuss the implications of our detailed study of this benchmark system for ultracold chemistry.

physics.atom-ph↗

arXiv2016

Milne's Equation revisited: Exact Asymptotic Solutions

We present novel approaches for solving Milne's equation, which was introduced in 1930 as an efficient numerical scheme for the Schrödinger equation. Milne's equation appears in a wide class of physical problems, ranging from astrophysics and cosmology, to quantum mechanics and quantum optics. We show how a third order linear differential equation is equivalent to Milne's non-linear equation, and can be used to accurately calculate Milne's amplitude and phase functions. We also introduce optimization schemes to achieve a convenient, fast, and accurate computation of wave functions using an economical parametrization. These new optimization procedures answer the long standing question of finding non-oscillatory solutions of Milne's equation. We apply them to long-range potentials and find numerically exact asymptotic solutions.

physics.atom-ph↗

arXiv2016

Near Threshold Effects on Recombination and Vibrational Relaxation in Efimov Systems

We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three-body recombination rate $K_3$ where three free atoms interact to produce an atom--dimer pair, and the relaxation rate $K_{\rm rel}$ where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for $K_3$, namely the NTR (Near Threshold Resonance) regime behavior $E^{-2}$ for negative scattering lengths and the NTS (Near Threshold Suppression) regime behavior $E^2$ for positive scattering lengths. We also confirm a previously found oscillatory behavior of $K_3$ at higher energy $E$. Finally, we find that $K_{\rm rel}$ behaves as $E^{-1}$ in the NTR regime.

physics.atom-ph↗

arXiv2016

Charge density wave with meronlike spin texture induced by a lateral superlattice in a two-dimensional electron gas

The combined effect of a lateral square superlattice potential and the Coulomb interaction on the ground state of a two-dimensional electron gas in a perpendicular magnetic field is studied for different rational values of $Γ$, the inverse of the number of flux quanta per unit cell of the external potential, at filling factor $ν=1$ in Landau level $N=0.$ When Landau level mixing and disorder effects are neglected, increasing the strength $W_{0}$ of the potential induces a transition, at a critical strength $W_{0}^{\left( c\right) },$ from a uniform and fully spin polarized state to a two-dimensional charge density wave (CDW) with a meronlike spin texture at each maximum and minimum of the CDW. The collective excitations of this vortex-CDW are similar to those of the Skyrme crystal that is expected to be the ground state near filling factor $ν=1$. In particular, a broken U(1) symmetry in the vortex-CDW results in an extra gapless phase mode that could provide a fast channel for the relaxation of nuclear spins. The average spin polarization $% S_{z}$ changes in a continuous or discontinuous manner as $W_{0}$ is increased depending on whether $Γ\in \left[ 1/2,1\right] $ or $Γ\in \left[ 0,1/2\right] .$ The phase mode and the meronlike spin texture disappear at large value of $W_{0},$ leaving as the ground state a partially spin-polarized CDW if $Γ\neq 1/2$ or a spin-unpolarized CDW if $Γ=1/2.$

cond-mat.mes-hall↗

arXiv2015

RD-NMR spectra of the crystal states of the two-dimensional electron gas in a quantizing magnetic field

Transport experiments on the two-dimensional electron gas (2DEG) confined into a semiconductor quantum well and subjected to a quantizing magnetic field have uncovered a rich variety of uniform and nonuniform phases such as the Laughlin liquids, the Wigner, bubble and Skyrme crystals and the quantum Hall stripe state. Optically pumped nuclear magnetic resonance (OP-NMR) has also been extremely useful in studying the magnetization and dynamics of electron solids with exotic spin textures such as the Skyrme crystal. Recently, it has been demonstrated that a related technique, resistively-detected nuclear magnetic resonance (RD-NMR), could be a good tool to study the topography of the electron solids in the fractional and integer quantum Hall regimes. In this work, we compute theoretically the RD-NMR line shapes of various crystal phases of the 2DEG and study the relation between their spin density and texture and their NMR spectra. This allows us to evaluate the ability of the RD-NMR to discriminate between the various types of crystal states.

cond-mat.mes-hall↗

arXiv2015

Electromagnetic absorption and Kerr effect in quantum Hall ferromagnetic states of bilayer graphene

In a quantizing magnetic field, the chiral two-dimensional electron gas in Landau level $N=0$ of bilayer graphene goes through a series of phase transitions at integer filling factors $ν\in \left[ -3,3\right] $ when the strength of an electric field applied perpendicularly to the layers is increased. At filling factor $ν=3,$ the electron gas can described by a simple two-level system where layer and spin degrees of freedom are frozen. The gas then behaves as an orbital quantum Hall ferromagnet. A Coulomb-induced Dzyaloshinskii-Moriya term in the orbital pseudospin Hamiltonian is responsible for a series of transitions first to a Wigner crystal state and then to a spiral state as the electric field is increased. Both states have a non trivial orbital pseudospin texture. In this work, we study how the phase diagram at $ν=3$ is modified by an electric field applied in the plane of the layers and then derive several experimental signatures of the uniform and nonuniform states in the phase diagram. In addition to the transport gap, we study the electromagnetic absorption and the Kerr rotation due to the excitations of the orbital pseudospin-wave modes in the broken-symmetry states.

cond-mat.mes-hall↗

arXiv2015

Effect of nuclear spin symmetry in cold and ultracold reactions: D + para/ortho-H$_2$

We report results for reaction and vibrational quenching of the collision D with para-H$_2$($v,j=0$) and ortho-H$_2$($v,j=1$) at cold and ultracold temperatures. We investigate the effect of nuclear spin symmetry for barrier dominated processes ($0\le v\le 4$) and for one barrierless case ($v=5$). We find resonant structures for energies in the range corresponding to 0.01--10 K, which depend on the nuclear spin of H$_2$, arising from contributions of specific partial waves. We discuss the implications on the results in this benchmark system for ultracold chemistry.

physics.chem-ph↗

arXiv2014

Transport gap and hysteretic behavior of the Ising quantum Hall ferromagnets in Landau levels $\left\vert N\right\vert >0$ of bilayer graphene

The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavior of the Ising quantum Hall ferromagnets. We compute the transport gap due to different excitations: bulk electron-hole pairs, electron-hole pairs confined to the coherent region of a valley-pseudospin domain wall, and spin or valley-pseudospin skyrmion-antiskyrmion pairs. We determine which of these excitations has the lowest energy at a given value of the Zeeman coupling, bias, and magnetic field.

cond-mat.mes-hall↗

arXiv2014

Ising quantum Hall ferromagnetism in Landau levels $\left\vert N\right\vert \geq 1$ of bilayer graphene

A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{ν}=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG is a valley or spin Ising quantum Hall ferromagnet. At odd fillings, the C2DEG is spin polarized and has all its electrons in one valley or the other. There is no intervalley coherence in contrast with most of the the ground states in Landau level $N=0.$ At even filling, $\widetilde{ν}=2,$ the C2DEG is either fully spin polarized with electrons occupying both valleys or spin unpolarized with electron occupying one of the two valleys. A finite electric field (or bias) applied perpendicularly to the plane of the C2DEG induces a series of first-order phase transitions between these different ground states. The transport gap or its slope is discontinuous at the bias where a transition occurs. Such discontinuity may result in a change in the transport properties of the C2DEG at that bias.

cond-mat.mes-hall↗

arXiv2014

Controlling ultracold chemical reactions via Rydberg-dressed interactions

We show that ultracold chemical reactions can be manipulated and controlled by using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasi-bound) states exist near the collision threshold. We investigate how, by Rydberg-dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmark system H$_2$+D, and show that resonances can be moved substantially and that rate coefficients at cold and ultracold temperatures can be increased by several orders of magnitude.

physics.atom-ph↗

arXiv2013

Validity of the two-band model of bilayer and trilayer graphene in a magnetic field

The eigenstates of an electron in the chiral two-dimensional electron gas (C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene is a spinor with $4$ or $6$ components respectively. These components give the amplitude of the wave function on the $4$ or $6$ carbon sites in the unit cell of the lattice. In the tight-binding approximation, the eigenenergies are thus found by diagonalizing a $4\times 4$ or a $6\times 6$ matrix. In the continuum approximation where the electron wave vector $% k<<1/a_{0},$ with $a_{0}$ the lattice constant of the graphene sheets, a common approximation is the two-band model\cite{McCann2006} (2BM)\ where the eigenstates for the bilayer and trilayer systems are described by a two-component spinor that gives the amplitude of the wave function on the two sites with low-energy $\left\vert E\right\vert <<γ_{1}$ where $% γ_{1}$ is the hopping energy between sites that are directly above one another in adjacent layers. The 2BM has been used extensively to study the phase diagram of the C2DEG in a magnetic field as well as its transport and optical properties. In this paper, we use a numerical approach to compute the eigenstates and Landau level energies of the full tight-binding model in the continuum approximation and compare them with the prediction of the 2BM when the magnetic field or an electrical bias between the outermost layers is varied. Our numerical analysis shows that the 2BM is a good approximation for bilayer graphene in a wide range of magnetic field and bias but mostly for Landau level $M=0.$ The applicability of the 2BM in trilayer graphene, even for level $M=0,$ is much more restricted. In this case, the 2BM\ fails to reproduce some of the level crossings that occur between the sub-levels of $M=0.$

cond-mat.mes-hall↗

arXiv2013

Threshold resonance effects in reactive processes

We investigate the effect of near threshold resonances in reactive scattering at low energy. We find a general type of anomalous behavior of the cross sections, and illustrate it with a real system (H$_2$ + Cl). For inelastic processes, the anomalous energy dependence of the total cross sections is given by $σ\sim\varepsilon^{-3/2}$. The standard threshold behavior given by Wigner's law ($σ\sim\varepsilon^{-1/2}$) is eventually recovered at vanishing energies, but its validity is now limited to a much narrower range of energies. The universal anomalous behavior leads to reaction rate coefficients behaving as $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime. We also provide analytical expressions for s-wave cross sections, and discuss the implication in ultracold physics and chemistry.

physics.atom-ph↗