Publications

Order by: publication date number of citations

• Density-operator evolution: Complete positivity and the Keldysh real-time expansion

  Viktor Reimer, Maarten Rolf Wegewijs

  SciPost Phys. 7, 012 (2019) · published 25 July 2019 | Toggle abstract · pdf

  We study the reduced time-evolution of open quantum systems by combining quantum-information and statistical field theory. Inspired by prior work [EPL 102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the explicit structure guaranteeing the complete positivity (CP) and trace-preservation (TP) of the real-time evolution expansion in terms of the microscopic system-environment coupling. This reveals a fundamental two-stage structure of the coupling expansion: Whereas the first stage defines the dissipative timescales of the system --before having integrated out the environment completely-- the second stage sums up elementary physical processes described by CP superoperators. This allows us to establish the nontrivial relation between the (Nakajima-Zwanzig) memory-kernel superoperator for the density operator and novel memory-kernel operators that generate the Kraus operators of an operator-sum. Importantly, this operational approach can be implemented in the existing Keldysh real-time technique and allows approximations for general time-nonlocal quantum master equations to be systematically compared and developed while keeping the CP and TP structure explicit. Our considerations build on the result that a Kraus operator for a physical measurement process on the environment can be obtained by 'cutting' a group of Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators lifted to the system plus environment which have a diagrammatic expansion in terms of time-nonlocal memory-kernel operators. These lifted Kraus operators obey coupled time-evolution equations which constitute an unraveling of the original Schr\"odinger equation for system plus environment. Whereas both equations lead to the same reduced dynamics, only the former explicitly encodes the operator-sum structure of the coupling expansion.

  8 citations

• Out of time ordered effective dynamics of a quartic oscillator

  Bidisha Chakrabarty, Soumyadeep Chaudhuri

  SciPost Phys. 7, 013 (2019) · published 29 July 2019 | Toggle abstract · pdf

  We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle.

  7 citations

• Thermal counting statistics in an atomic two-mode squeezed vacuum state

  Maxime Perrier, Ziyad Amodjee, Pierre Dussarrat, Alexandre Dareau, Alain Aspect, Marc Cheneau, Denis Boiron, Christoph I. Westbrook

  SciPost Phys. 7, 002 (2019) · published 3 July 2019 | Toggle abstract · pdf

  We measure the population distribution in one of the atomic twin beams generated by four-wave mixing in an optical lattice. Although the produced two-mode squeezed vacuum state is pure, each individual mode is described as a statistical mixture. We confirm the prediction that the particle number follows an exponential distribution when only one spatio-temporal mode is selected. We also show that this distribution accounts well for the contrast of an atomic Hong--Ou--Mandel experiment. These experiments constitute an important validation of our twin beam source in view of a future test of a Bell inequality.

  6 citations

• Quantum walks on graphs of the ordered Hamming scheme and spin networks

  Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet

  SciPost Phys. 7, 001 (2019) · published 2 July 2019 | Toggle abstract · pdf

  It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.

  3 citations