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Papers by Peter Littlewood

Research paper thumbnail of A functional approach to polariton quantum crystals

Physica B: Condensed Matter, 2015

Research paper thumbnail of Superconductivity: The persistence of pairs

Research paper thumbnail of Amplitude-mode dynamics of polariton condensates

Physical review letters, Jan 22, 2011

We study the stability of collective amplitude excitations in nonequilibrium polariton condensate... more We study the stability of collective amplitude excitations in nonequilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wave vectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.

Research paper thumbnail of Phenomenology of the superconductive state of a marginal Fermi liquid

Physical review. B, Condensed matter, 1992

We consider an extension of the marginal-Fermi-liquid model to the s-wave superconducting state b... more We consider an extension of the marginal-Fermi-liquid model to the s-wave superconducting state by phenomenologically incorporating the superconducting gap into the scattering spectrum. The linear-intemperature scattering rate due to the high density of low-energy electronic excitations naturally leads to a large pair-breaking rate, which suppresses T, . Below T, the low-energy excitations are selfconsistently suppressed due to the opening of a superconducting gap. This leads to a vanishing of both the inelastic-scattering rate and pair breaking below T, . There are a number of consequences not found in traditional BCS electron-phonon-induced s-wave superconductors. For energies below 3h, the quasiparticles become well defined in the superconducting state, while they are marginal (scattering rate proportional to the energy) in the normal state. This produces a two-peaked structure in the one-particle spectraa sharp feature between 5 and 3h (depending on momentum) and a broad hump with an onset at 3h (independent of momentum). The transport properties do not obey the usual BCS rules. Transport properties in the q~0 limit and for low frequencies co && 6 show peaks below T, . These are observable in microwave conductivity and in electronic thermal conductivity. Local or momentum-averaged response properties such as the nuclear relaxation rate show no peak, but a sharp drop below T, . The superconductive gap opens very rapidly below T"and the value of 2L/T, can cover a wide range, depending on parameters. The physical origin of these results is discussed, and comparison to experiment is made.

Research paper thumbnail of Pairing by dynamic charge fluctuations in the extended Hubbard model

Physical review. B, Condensed matter, 1990

We consider superconductivity mediated by a charge-transfer resonance (CTR) in the weak-coupling ... more We consider superconductivity mediated by a charge-transfer resonance (CTR) in the weak-coupling approach to the three-band extended Hubbard model for the copper oxide superconductors. Our effective pairing interaction contains the dynamics of the CTR, and local-field effects. Unlike previous work, we solve the linearized Eliashberg equations on the lattice while retaining the full momentum dependence of the interaction and wave

Research paper thumbnail of Freezing electronic correlations by polaronic instabilities in doped La2NiO4

Physical review. B, Condensed matter, 1994

Research paper thumbnail of Screening of Strain Fields in Manganites

Research paper thumbnail of Many-body Physics of Rydberg Polaritons

Research paper thumbnail of Machine Learning for Dynamical Mean Field Theory

Research paper thumbnail of Quantum Melting in a Polariton Lattice

Quantum Melting in a Polariton Lattice ALEXANDER EDELMAN, PETER LITTLEWOOD, Univ of Chicago -We s... more Quantum Melting in a Polariton Lattice ALEXANDER EDELMAN, PETER LITTLEWOOD, Univ of Chicago -We study a generalized Dicke model of lattice polaritons, with a pair-potential interaction between excited states of the spin component, in the functional integral formalism. Even considering only zerotemperature equilibrium effects with a uniform photon field, there is a rich phase diagram as a function of light-matter coupling, which includes spatially ordered and superfluid phases. Depending sensitively on the form of the potential, the interaction may induce an instability in the sound mode of the polariton condensate, or destroy the condensate altogether. Zero-temperature fluctuations may likewise melt the spatially ordered phases. We consider implications for cold-atom experiments with tunable interactions, as well as interacting exciton-polaritons accessible in the solid state.

Research paper thumbnail of Nonlinear Conductivity of a 2-DIMENSIONAL Pinned Charge-Density Wavein a Strong Magnetic-Field

Research paper thumbnail of Magnetic-Field-Induced Localization Transition in Hgcdte-Response

We have performed magnetoresistance and Hall-resistance measurements on low-carrier-concentration... more We have performed magnetoresistance and Hall-resistance measurements on low-carrier-concentration n-type samples of Hg0.76Cd0.24Te at millikelvin temperatures. We observe an abrupt rise in the Hall resistance and magnetoresistance at a characteristic field Hc which is a significant function of temperature and which allows us to reject magnetic freezeout or localization by disorder as possible mechanisms. We believe our data provide compelling evidence for a model involving magnetic freezeout into a three-dimensional Wigner lattice.

Research paper thumbnail of Paraelectric and ferroelectric states in a model for relaxor ferroelectrics

Research paper thumbnail of Magnetism and metal-insulator transition in oxygen deficient SrTi0 $ _3$

Research paper thumbnail of Schrödinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed ... more We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrödinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication.

Research paper thumbnail of Semiconductor neutron detector

A neutron detector has a compound of lithium in a single crystal form as a neutron sensor element... more A neutron detector has a compound of lithium in a single crystal form as a neutron sensor element. The lithium compound, containing improved charge transport properties, is either lithium niobate or lithium tantalate. The sensor element is in direct contact with a monitor that detects an electric current. A signal proportional to the electric current is produced and is calibrated

Research paper thumbnail of Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions

We connect three phenomena in which a coherent electromagnetic field could be generated: polarito... more We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using Dicke-type models of spins coupled to a single photon mode. These descriptions may be distinguished by whether the spins are quantum or classical, and whether they are strongly or weakly damped.

Research paper thumbnail of Modeling quantum physics with machine learning

Research paper thumbnail of Polariton condensation with saturable molecules dressed by vibrational modes

Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopical... more Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopically coherent state at low temperatures or high densities. Recent experiments show that coupling light to organic molecules inside a microcavity allows condensation at room temperature. The molecules act as saturable absorbers with transitions dressed by molecular vibrational modes. Motivated by this, we calculate the phase diagram and spectrum of a modified Tavis-Cummings model, describing vibrationally dressed two-level systems, coupled to a cavity mode. Coupling to vibrational modes can induce re-entrance, i.e. a normal-condensed-normal sequence with decreasing temperature and can drive the transition first-order.

Research paper thumbnail of Excitons in T-shaped quantum wires

Physical Review B, 2001

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave fu... more We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/AlxGa1−xAs and InyGa1−yAs/AlxGa1−xAs structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction x. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/AlxGa1−xAs wires we obtain an upper limit for the binding energy of around 25 meV in a 10Å wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that InyGa1−yAs/AlxGa1−xAs might be a good candidate.

Research paper thumbnail of A functional approach to polariton quantum crystals

Physica B: Condensed Matter, 2015

Research paper thumbnail of Superconductivity: The persistence of pairs

Research paper thumbnail of Amplitude-mode dynamics of polariton condensates

Physical review letters, Jan 22, 2011

We study the stability of collective amplitude excitations in nonequilibrium polariton condensate... more We study the stability of collective amplitude excitations in nonequilibrium polariton condensates. These excitations correspond to renormalized upper polaritons and to the collective amplitude modes of atomic gases and superconductors. They would be present following a quantum quench or could be created directly by resonant excitation. We show that uniform amplitude excitations are unstable to the production of excitations at finite wave vectors, leading to the formation of density-modulated phases. The physical processes causing the instabilities can be understood by analogy to optical parametric oscillators and the atomic Bose supernova.

Research paper thumbnail of Phenomenology of the superconductive state of a marginal Fermi liquid

Physical review. B, Condensed matter, 1992

We consider an extension of the marginal-Fermi-liquid model to the s-wave superconducting state b... more We consider an extension of the marginal-Fermi-liquid model to the s-wave superconducting state by phenomenologically incorporating the superconducting gap into the scattering spectrum. The linear-intemperature scattering rate due to the high density of low-energy electronic excitations naturally leads to a large pair-breaking rate, which suppresses T, . Below T, the low-energy excitations are selfconsistently suppressed due to the opening of a superconducting gap. This leads to a vanishing of both the inelastic-scattering rate and pair breaking below T, . There are a number of consequences not found in traditional BCS electron-phonon-induced s-wave superconductors. For energies below 3h, the quasiparticles become well defined in the superconducting state, while they are marginal (scattering rate proportional to the energy) in the normal state. This produces a two-peaked structure in the one-particle spectraa sharp feature between 5 and 3h (depending on momentum) and a broad hump with an onset at 3h (independent of momentum). The transport properties do not obey the usual BCS rules. Transport properties in the q~0 limit and for low frequencies co && 6 show peaks below T, . These are observable in microwave conductivity and in electronic thermal conductivity. Local or momentum-averaged response properties such as the nuclear relaxation rate show no peak, but a sharp drop below T, . The superconductive gap opens very rapidly below T"and the value of 2L/T, can cover a wide range, depending on parameters. The physical origin of these results is discussed, and comparison to experiment is made.

Research paper thumbnail of Pairing by dynamic charge fluctuations in the extended Hubbard model

Physical review. B, Condensed matter, 1990

We consider superconductivity mediated by a charge-transfer resonance (CTR) in the weak-coupling ... more We consider superconductivity mediated by a charge-transfer resonance (CTR) in the weak-coupling approach to the three-band extended Hubbard model for the copper oxide superconductors. Our effective pairing interaction contains the dynamics of the CTR, and local-field effects. Unlike previous work, we solve the linearized Eliashberg equations on the lattice while retaining the full momentum dependence of the interaction and wave

Research paper thumbnail of Freezing electronic correlations by polaronic instabilities in doped La2NiO4

Physical review. B, Condensed matter, 1994

Research paper thumbnail of Screening of Strain Fields in Manganites

Research paper thumbnail of Many-body Physics of Rydberg Polaritons

Research paper thumbnail of Machine Learning for Dynamical Mean Field Theory

Research paper thumbnail of Quantum Melting in a Polariton Lattice

Quantum Melting in a Polariton Lattice ALEXANDER EDELMAN, PETER LITTLEWOOD, Univ of Chicago -We s... more Quantum Melting in a Polariton Lattice ALEXANDER EDELMAN, PETER LITTLEWOOD, Univ of Chicago -We study a generalized Dicke model of lattice polaritons, with a pair-potential interaction between excited states of the spin component, in the functional integral formalism. Even considering only zerotemperature equilibrium effects with a uniform photon field, there is a rich phase diagram as a function of light-matter coupling, which includes spatially ordered and superfluid phases. Depending sensitively on the form of the potential, the interaction may induce an instability in the sound mode of the polariton condensate, or destroy the condensate altogether. Zero-temperature fluctuations may likewise melt the spatially ordered phases. We consider implications for cold-atom experiments with tunable interactions, as well as interacting exciton-polaritons accessible in the solid state.

Research paper thumbnail of Nonlinear Conductivity of a 2-DIMENSIONAL Pinned Charge-Density Wavein a Strong Magnetic-Field

Research paper thumbnail of Magnetic-Field-Induced Localization Transition in Hgcdte-Response

We have performed magnetoresistance and Hall-resistance measurements on low-carrier-concentration... more We have performed magnetoresistance and Hall-resistance measurements on low-carrier-concentration n-type samples of Hg0.76Cd0.24Te at millikelvin temperatures. We observe an abrupt rise in the Hall resistance and magnetoresistance at a characteristic field Hc which is a significant function of temperature and which allows us to reject magnetic freezeout or localization by disorder as possible mechanisms. We believe our data provide compelling evidence for a model involving magnetic freezeout into a three-dimensional Wigner lattice.

Research paper thumbnail of Paraelectric and ferroelectric states in a model for relaxor ferroelectrics

Research paper thumbnail of Magnetism and metal-insulator transition in oxygen deficient SrTi0 $ _3$

Research paper thumbnail of Schrödinger equation with a spatially and temporally random potential: Effects of cross-phase modulation in optical communication

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed ... more We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schrödinger equation with a spatially and temporally random potential. Green's functions for the propagation of light in this system are calculated using Feynman path-integral and diagrammatic techniques. This propagation leads to a non-Gaussian joint distribution of the input and output optical fields. We use these results to determine the amplitude and timing jitter of a signal pulse and to estimate the system capacity in analog communication.

Research paper thumbnail of Semiconductor neutron detector

A neutron detector has a compound of lithium in a single crystal form as a neutron sensor element... more A neutron detector has a compound of lithium in a single crystal form as a neutron sensor element. The lithium compound, containing improved charge transport properties, is either lithium niobate or lithium tantalate. The sensor element is in direct contact with a monitor that detects an electric current. A signal proportional to the electric current is produced and is calibrated

Research paper thumbnail of Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions

We connect three phenomena in which a coherent electromagnetic field could be generated: polarito... more We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using Dicke-type models of spins coupled to a single photon mode. These descriptions may be distinguished by whether the spins are quantum or classical, and whether they are strongly or weakly damped.

Research paper thumbnail of Modeling quantum physics with machine learning

Research paper thumbnail of Polariton condensation with saturable molecules dressed by vibrational modes

Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopical... more Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopically coherent state at low temperatures or high densities. Recent experiments show that coupling light to organic molecules inside a microcavity allows condensation at room temperature. The molecules act as saturable absorbers with transitions dressed by molecular vibrational modes. Motivated by this, we calculate the phase diagram and spectrum of a modified Tavis-Cummings model, describing vibrationally dressed two-level systems, coupled to a cavity mode. Coupling to vibrational modes can induce re-entrance, i.e. a normal-condensed-normal sequence with decreasing temperature and can drive the transition first-order.

Research paper thumbnail of Excitons in T-shaped quantum wires

Physical Review B, 2001

We calculate energies, oscillator strengths for radiative recombination, and two-particle wave fu... more We calculate energies, oscillator strengths for radiative recombination, and two-particle wave functions for the ground state exciton and around 100 excited states in a T-shaped quantum wire. We include the single-particle potential and the Coulomb interaction between the electron and hole on an equal footing, and perform exact diagonalisation of the two-particle problem within a finite basis set. We calculate spectra for all of the experimentally studied cases of T-shaped wires including symmetric and asymmetric GaAs/AlxGa1−xAs and InyGa1−yAs/AlxGa1−xAs structures. We study in detail the shape of the wave functions to gain insight into the nature of the various states for selected symmetric and asymmetric wires in which laser emission has been experimentally observed. We also calculate the binding energy of the ground state exciton and the confinement energy of the 1D quantum-wire-exciton state with respect to the 2D quantum-well exciton for a wide range of structures, varying the well width and the Al molar fraction x. We find that the largest binding energy of any wire constructed to date is 16.5 meV. We also notice that in asymmetric structures, the confinement energy is enhanced with respect to the symmetric forms with comparable parameters but the binding energy of the exciton is then lower than in the symmetric structures. For GaAs/AlxGa1−xAs wires we obtain an upper limit for the binding energy of around 25 meV in a 10Å wide GaAs/AlAs structure which suggests that other materials must be explored in order to achieve room temperature applications. There are some indications that InyGa1−yAs/AlxGa1−xAs might be a good candidate.