TY - JOUR
AB - We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.
AU - Giuliani, Alessandro
AU - Robert Seiringer
ID - 2384
IS - 5-6
JF - Journal of Statistical Physics
TI - The ground state energy of the weakly interacting Bose gas at high density
VL - 135
ER -
TY - JOUR
AB - We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity, so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground-state energy of the corresponding N -body Hamiltonian with contact interaction provided the total angular momentum L is much less than N2. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground-state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.
AU - Lieb, Élliott H
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2385
IS - 6
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Yrast line of a rapidly rotating Bose gas: Gross-Pitaevskii regime
VL - 79
ER -
TY - JOUR
AB - We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2 ρ is small and the temperature T satisfies T> 4πρ ln | ln (a2 ρ) |. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T- Tc (0) Tc (0) >5 a ρ1/3, where Tc (0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.
AU - Robert Seiringer
AU - Ueltschi, Daniel
ID - 2386
IS - 1
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Rigorous upper bound on the critical temperature of dilute Bose gases
VL - 80
ER -
TY - JOUR
AB - We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.
AU - Lewin, Mathieu
AU - Robert Seiringer
ID - 2387
IS - 5
JF - Journal of Statistical Physics
TI - Strongly correlated phases in rapidly rotating Bose gases
VL - 137
ER -
TY - JOUR
AB - This paper provides self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifies the connection of coherence and proper scoring rules to Bregman divergence.
AU - Predd, Joel B
AU - Robert Seiringer
AU - Lieb, Élliott H
AU - Osherson, Daniel N
AU - Poor, Harold V
AU - Kulkarni, Sanjeev R
ID - 2388
IS - 10
JF - IEEE Transactions on Information Theory
TI - Probabilistic coherence and proper scoring rules
VL - 55
ER -
TY - CONF
AB - Let EMBEDk→d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k, does there exist a (piecewise linear) embedding of K into ℝd? Known results easily imply polynomiality of EMBEDk→2 (k = 1, 2; the case k = 1, d = 2 is graph planarity) and of EMBEDk→2k for all k ≥ 3 (even if k is not considered fixed). We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that EMBED d→d and EMBED(d-1)→d are undecidable for each d ≥ 5. Our main result is NP-hardness of EMBED2→4 and, more generally, of EMBEDk→d for all k, d with d ≥ 4 and d ≥ k ≥ (2d - 2)/3.
AU - Matoušek, Jiří
AU - Martin Tancer
AU - Uli Wagner
ID - 2433
TI - Hardness of embedding simplicial complexes in ℝd
ER -
TY - JOUR
AB - G protein-coupled receptors (GPCRs) have critical functions in intercellular communication. Although a wide range of different receptors have been identified in the same cells, the mechanism by which signals are integrated remains elusive. The ability of GPCRs to form dimers or larger hetero-oligomers is thought to generate such signal integration. We examined the molecular mechanisms responsible for the GABAB receptor-mediated potentiation of the mGlu receptor signalling reported in Purkinje neurons. We showed that this effect does not require a physical interaction between both receptors. Instead, it is the result of a more general mechanism in which the βγ subunits produced by the Gi-coupled GABAB receptor enhance the mGlu-mediated Gq response. Most importantly, this mechanism could be generally applied to other pairs of Gi- and Gq-coupled receptors and the signal integration varied depending on the time delay between activation of each receptor. Such a mechanism helps explain specific properties of cells expressing two different Gi- and Gq-coupled receptors activated by a single transmitter, or properties of GPCRs naturally coupled to both types of the G protein.
AU - Rives, Marie L
AU - Vol, Claire
AU - Fukazawa, Yugo
AU - Tinel, Norbert
AU - Trinquet, Eric
AU - Ayoub, Mohammed A
AU - Ryuichi Shigemoto
AU - Pin, Jean-Philippe
AU - Prezèau, Laurent
ID - 2499
IS - 15
JF - EMBO Journal
TI - Crosstalk between GABAB and mGlu1a receptors reveals new insight into GPCR signal integration
VL - 28
ER -
TY - JOUR
AB - Recent theoretical work has provided a basic understanding of signal propagation in networks of spiking neurons, but mechanisms for gating and controlling these signals have not been investigated previously. Here we introduce an idea for the gating of multiple signals in cortical networks that combines principles of signal propagation with aspects of balanced networks. Specifically, we studied networks in which incoming excitatory signals are normally cancelled by locally evoked inhibition, leaving the targeted layer unresponsive. Transmission can be gated 'on' by modulating excitatory and inhibitory gains to upset this detailed balance. We illustrate gating through detailed balance in large networks of integrate-and-fire neurons. We show successful gating of multiple signals and study failure modes that produce effects reminiscent of clinically observed pathologies. Provided that the individual signals are detectable, detailed balance has a large capacity for gating multiple signals.
AU - Vogels, Tim P
AU - Abbott, L F
ID - 8026
IS - 4
JF - Nature Neuroscience
SN - 1097-6256
TI - Gating multiple signals through detailed balance of excitation and inhibition in spiking networks
VL - 12
ER -
TY - JOUR
AB - We have developed a tunable source of Mie scale microdroplet aerosols that can be used for the generation of energetic ions. To demonstrate this potential, a terawatt Ti: Al2 O3 laser focused to 2×10 19 W/cm2 was used to irradiate heavy water (D2 O) aerosols composed of micron-scale droplets. Energetic deuterium ions, which were generated in the laser-droplet interaction, produced deuterium-deuterium fusion with approximately 2×10^3 fusion neutrons measured per joule of incident laser energy.
AU - Higginbotham, Andrew P
AU - Semonin, Octavi
AU - Bruce, S
AU - Chan, C
AU - Maindi, M
AU - Donnelly, Tom
AU - Maurer, M
AU - Bang, Woosuk
AU - Churina, I.V
AU - Osterholz, Jens
AU - Kim, I
AU - Bernstein, Aaron
AU - Ditmire, Todd
ID - 88
IS - 6
JF - Review of Scientific Instruments
TI - Generation of Mie size microdroplet aerosols with applications in laser-driven fusion experiments
VL - 80
ER -
TY - JOUR
AB - We demonstrate the time-resolved driving of two-photon blue sideband transitions between superconducting qubits and a transmission line resonator. As an example of using these sideband transitions for a two-qubit operation, we implement a pulse sequence that first entangles one qubit with the resonator and subsequently distributes the entanglement between two qubits. We show the generation of 75% fidelity Bell states by this method. The full density matrix of the two-qubit system is extracted using joint measurement and quantum state tomography and shows close agreement with numerical simulation.
AU - Leek, Peter J
AU - Filipp, Stefan
AU - Maurer, Patrick
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Johannes Fink
AU - Göppl, M
AU - Steffen, L. Kraig
AU - Wallraff, Andreas
ID - 1766
IS - 18
JF - Physical Review B - Condensed Matter and Materials Physics
TI - Using sideband transitions for two-qubit operations in superconducting circuits
VL - 79
ER -
TY - JOUR
AB - We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive readout of the qubit coupled off resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited qubit states and dispersive level shifts due to off-resonant drives.
AU - Baur, Matthias P
AU - Filipp, Stefan
AU - Bianchetti, R
AU - Johannes Fink
AU - Göppl, M
AU - Steffen, L. Kraig
AU - Leek, Peter J
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1767
IS - 24
JF - Physical Review Letters
TI - Measurement of autler-townes and mollow transitions in a strongly driven superconducting qubit
VL - 102
ER -
TY - JOUR
AB - Quantum state tomography is an important tool in quantum information science for complete characterization of multiqubit states and their correlations. Here we report a method to perform a joint simultaneous readout of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The nonlinear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single-shot readout of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.
AU - Filipp, Stefan
AU - Maurer, Patrick
AU - Leek, Peter J
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Johannes Fink
AU - Göppl, M
AU - Steffen, L. Kraig
AU - Gambetta, Jay M
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1768
IS - 20
JF - Physical Review Letters
TI - Two-qubit state tomography using a joint dispersive readout
VL - 102
ER -
TY - JOUR
AB - We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two, and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multiqubit states and observe the discrete N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multiatom quantum optics experiments with fixed atom numbers.
AU - Johannes Fink
AU - Bianchetti, R
AU - Baur, Matthias P
AU - Göppl, M
AU - Steffen, L. Kraig
AU - Filipp, Stefan
AU - Leek, Peter J
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1769
IS - 8
JF - Physical Review Letters
TI - Dressed collective qubit states and the Tavis-Cummings model in circuit QED
VL - 103
ER -
TY - JOUR
AB - The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements.
AU - Bianchetti, R
AU - Filipp, Stefan
AU - Baur, Matthias P
AU - Johannes Fink
AU - Göppl, M
AU - Leek, Peter J
AU - Steffen, L. Kraig
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1770
IS - 4
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics
VL - 80
ER -
TY - JOUR
AB - The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Our data indicate that the role of thermal fields in resonant cavity QED can be studied in detail using superconducting circuits.
AU - Johannes Fink
AU - Baur, Matthias P
AU - Bianchetti, R
AU - Filipp, Stefan
AU - Göppl, M
AU - Leek, Peter J
AU - Steffen, L. Kraig
AU - Blais, Alexandre
AU - Wallraff, Andreas
ID - 1771
JF - Physica Scripta T
TI - Thermal excitation of multi-photon dressed states in circuit quantum electrodynamics
VL - T137
ER -
TY - JOUR
AB - Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus. A key mechanism that underlies this response is the slow, activity-dependent removal of responding molecules to a pool which is unavailable to respond immediately to the input. This mechanism is implemented in different ways in various biological systems and has traditionally been studied separately for each. Here we highlight the common aspects of this principle, shared by many biological systems, and suggest a unifying theoretical framework. We study theoretically a class of models which describes the general mechanism and allows us to distinguish its universal from system-specific features. We show that under general conditions, regardless of the details of kinetics, molecule availability encodes an averaging over past activity and feeds back multiplicatively on the system output. The kinetics of recovery from unavailability determines the effective memory kernel inside the feedback branch, giving rise to a variety of system-specific forms of adaptive response—precise or input-dependent, exponential or power-law—as special cases of the same model.
AU - Tamar Friedlander
AU - Brenner, Naama
ID - 1825
IS - 52
JF - PNAS
TI - Adaptive response by state-dependent inactivation
VL - 106
ER -
TY - JOUR
AB - Let (E, H, μ) be an abstract Wiener space and let DV : = V D, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space under(H, {combining low line}). Given a bounded operator B on under(H, {combining low line}), coercive on the range over(R (V), -), we consider the operators A : = V* B V in H and under(A, {combining low line}) : = V V* B in under(H, {combining low line}), as well as the realisations of the operators L : = DV* B DV and under(L, {combining low line}) : = DV DV* B in Lp (E, μ) and Lp (E, μ ; under(H, {combining low line})) respectively, where 1 < p < ∞. Our main result asserts that the following four assertions are equivalent: (1)D (sqrt(L)) = D (DV) with {norm of matrix} sqrt(L) f {norm of matrix}p {minus tilde} {norm of matrix} DV f {norm of matrix}p for f ∈ D (sqrt(L));(2)under(L, {combining low line}) admits a bounded H∞-functional calculus on over(R (DV), -);(3)D (sqrt(A)) = D (V) with {norm of matrix} sqrt(A) h {norm of matrix} {minus tilde} {norm of matrix} V h {norm of matrix} for h ∈ D (sqrt(A));(4)under(A, {combining low line}) admits a bounded H∞-functional calculus on over(R (V), -). Moreover, if these conditions are satisfied, then D (L) = D (DV2) ∩ D (DA). The equivalence (1)-(4) is a non-symmetric generalisation of the classical Meyer inequalities of Malliavin calculus (where under(H, {combining low line}) = H, V = I, B = frac(1, 2) I). A one-sided version of (1)-(4), giving Lp-boundedness of the Riesz transform DV / sqrt(L) in terms of a square function estimate, is also obtained. As an application let -A generate an analytic C0-contraction semigroup on a Hilbert space H and let -L be the Lp-realisation of the generator of its second quantisation. Our results imply that two-sided bounds for the Riesz transform of L are equivalent with the Kato square root property for A. The boundedness of the Riesz transform is used to obtain an Lp-domain characterisation for the operator L.
AU - Jan Maas
AU - van Neerven, Jan M
ID - 2119
IS - 8
JF - Journal of Functional Analysis
TI - Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces
VL - 257
ER -
TY - JOUR
AB - Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A (2009) in press], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential.
AU - Mikhail Lemeshko
AU - Frierich, Bretislav
ID - 2137
IS - 1
JF - Journal of Atomic and Molecular Sciences
TI - Rotational structure of weakly bound molecular ions
VL - 1
ER -
TY - JOUR
AB - We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules (Σ2, Σ3, and Π2) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. 129, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. 280, 19 (2009)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He-CaH (XΣ+2), He-O2 (XΣ–3), and He-OH (XΠΩ2) systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He-OH system, weak for the He-CaH collisions, and strong for the He-O2. While odd ΔM transitions dominate the He-OH [J=3/2,f→J′,e/f] integral cross sections in a magnetic field parallel to the relative velocity vector, even ΔM transitions prevail in the case of the He-CaH (X2Σ+) and He-O2 (XΣ−3) collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions N=1,J=0→N′, J′ with J′=N′.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2149
IS - 1
JF - Physical Review A - Atomic, Molecular, and Optical Physics
TI - Collisions of paramagnetic molecules in magnetic fields: An analytic model based on Fraunhofer diffraction of matter waves
VL - 79
ER -
TY - JOUR
AB - We examine the effects of a linearly polarized nonresonant radiative field on the dynamics of rotationally inelastic Na+ + N2 collisions at eV collision energies. Our treatment is based on the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric fields [M. Lemeshko, B. Friedrich, J. Chem. Phys. 129 (2008) 024301]. The nonresonant radiative field changes the effective shape of the target molecule by aligning it in the space-fixed frame. This markedly alters the differential and integral scattering cross-sections. As the cross-sections can be evaluated for a polarization of the radiative field collinear or perpendicular to the relative velocity vector, the model also offers predictions about steric asymmetry of the collisions.
AU - Mikhail Lemeshko
AU - Friedrich, Břetislav
ID - 2150
IS - 1-3
JF - International Journal of Mass Spectrometry
TI - The effect of a nonresonant radiative field on low-energy rotationally inelastic Na+ + N2 collisions
VL - 280
ER -