András Vukics

Prospects for the cavity-assisted laser cooling of molecules

Cooling of molecules via free-space dissipative scattering of photons is thought not to be practicable due to the inherently large number of Raman loss channels available to molecules and the prohibitive expense of building multiple-repumping laser systems. The use of an optical cavity to enhance coherent Rayleigh scattering into a decaying cavity mode has been suggested as a potential method to mitigate Raman loss, thereby enabling the laser cooling of molecules to ultracold temperatures. We discuss the possibility of cavity-assisted laser cooling of particles without closed transitions, identify conditions necessary to achieve efficient cooling, and suggest solutions given experimental constraints. Specifically, it is shown that cooperativities much greater than unity are required for cooling without loss, and that this could be achieved via the superradiant scattering associated with intracavity self-localization of the molecules. Particular emphasis is given to the polar hydroxyl radical (OH), cold samples of which are readily obtained from Stark deceleration.

C++QED : an object-oriented framework for wave-function simulations of cavity QED systems

Abstract.We present a framework for efficiently performing Monte Carlo wave-function simulations in cavity QED with moving particles. It relies heavily on the object-oriented programming paradigm as realised in C++, and is extensible and applicable for simulating open interacting qua ntum dynamics in general. The user is provided with a number of “elements”, e.g. pumped moving particles, pumped lossy cavity modes, and various interactions to compose complex interacting systems, which contain several particles moving in electromagnetic fields of various configurations, and perform wave-function simulations on such systems. A number of tools are provided to facilitate the implementation of new elements.

Observation of the photon-blockade breakdown phase transition

Non-equilibrium phase transitions exist in damped-driven open quantum systems, when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can co-exist in a critical hysteresis domain. Here we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics (QED) system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the milli-second range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multi-photon quantum many-body phases.

Elimination of the A-square problem from cavity QED.

We generalize the Power-Zineau-Woolley transformation to obtain a canonical Hamiltonian of cavity quantum electrodynamics for arbitrary geometry of boundaries. This Hamiltonian is free from the A-square term and the instantaneous Coulomb interaction between distinct atoms. The single-mode models of cavity QED (Dicke, Tavis-Cummings, Jaynes-Cummings) are justified by a term by term mapping to the proposed microscopic Hamiltonian. As one straightforward consequence, the basis of no-go argumentations concerning the Dicke phase transition with atoms in electromagnetic fields dissolves.

Microscopic physics of quantum self-organization of optical lattices in cavities

We study quantum particles at zero temperature in an optical lattice coupled to a resonant cavity mode. The cavity field substantially modifies the particle dynamics in the lattice, and for strong particle-field coupling leads to self-organization of the particles, a configuration with only every second site occupied. We study the growth of this order out of a homogeneous initial distribution for few particles. Simulations reveal that the growth dynamics crucially depends on the initial quantum many-body state of the particles and can be monitored via the cavity fluorescence. Studying the relaxation time of the ordering reveals inhibited tunnelling due to the interaction with the cavity field. However, the relaxation becomes very quick for strong coupling.

Fundamental limitation of ultrastrong coupling between light and atoms

In a recent work of ours [Phys. Rev. Lett. 112, 073601 (2014)], we generalized the Power-Zineau-Woolley gauge to describe the electrodynamics of atoms in an arbitrary confined geometry. Here we complement the theory by proposing a tractable form of the polarization field to represent atomic material with well-defined intra-atomic potential. The direct electrostatic dipole-dipole interaction between the atoms is canceled. This theory yields a suitable framework to determine limitations on the light-matter coupling in quantum optical models with discernible atoms. We find that the superradiant criticality is at the border of covalent molecule formation and crystallization.

Optical bistability in strong-coupling cavity QED with a few atoms

We present exact numerical solutions of the damped-driven Jaynes–Cummings model adapted to describe absorptive optical bistability in the limit of a few atoms strongly coupled to a high-finesse resonator. We show that the simplifying semiclassical result for many physical quantities of interest is well reproduced by the quantum model including even with only a few atoms in the strongly coupled system. Non-trivial atom–field quantum cross-correlations show up in the strong-driving limit.

Cavity nonlinear optics with few photons and ultracold quantum particles

The light force on particles trapped in the field of a high-Q cavity mode depends on the quantum state of field and particle. Different photon numbers generate different optical potentials anddifferent motional states induce different field evolution. Even for weak saturation and linear polarizability the induced particle motion leads to nonlinear field dynamics. We derive a corresponding effective field Hamiltonian containing all the powers of the photon number operator, which predicts nonlinear phase shifts and squeezing even at the few-photon level. Wave-function simulations of the full particle-field dynamics confirm this and show significant particle-field entanglement in addition.

C++QEDv2: The multi-array concept and compile-time algorithms in the definition of composite quantum systems

Abstract C++QED is a versatile framework for simulating open quantum dynamics. It allows to build arbitrarily complex quantum systems from elementary free subsystems and interactions, and simulate their time evolution with the available time-evolution drivers. Through this framework, we introduce a design which should be generic for high-level representations of composite quantum systems. It relies heavily on the object-oriented and generic programming paradigms on one hand, and on the other hand, compile-time algorithms, in particular C++ template-metaprogramming techniques. The core of the design is the data structure which represents the state vectors of composite quantum systems. This data structure models the multi-array concept. The use of template metaprogramming is not only crucial to the design, but with its use all computations pertaining to the layout of the simulated system can be shifted to compile time, hence cutting on runtime. Program summary Program title: C++QED Catalogue identifier: AELU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELU_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: http://cpc.cs.qub.ac.uk/licence/aelu_v1_0.html . The C++QED package contains other software packages, Blitz, Boost and FLENS, all of which may be distributed freely but have individual license requirements. Please see individual packages for license conditions. No. of lines in distributed program, including test data, etc.: 597 974 No. of bytes in distributed program, including test data, etc.: 4 874 839 Distribution format: tar.gz Programming language: C++ Computer: i386–i686, x86_64 Operating system: In principle cross-platform, as yet tested only on UNIX-like systems (including Mac OS X). RAM: The framework itself takes about 60 MB, which is fully shared. The additional memory taken by the program which defines the actual physical system (script) is typically less than 1 MB. The memory storing the actual data scales with the system dimension for state-vector manipulations, and the square of the dimension for density-operator manipulations. This might easily be GBs, and often the memory of the machine limits the size of the simulated system. Classification: 4.3, 4.13, 6.2, 20 External routines: Boost C++ libraries ( http://www.boost.org/ ), GNU Scientific Library ( http://www.gnu.org/software/gsl/ ), Blitz++ ( http://www.oonumerics.org/blitz/ ), Linear Algebra Package – Flexible Library for Efficient Numerical Solutions ( http://flens.sourceforge.net/ ). Nature of problem: Definition of (open) composite quantum systems out of elementary building blocks [1]. Manipulation of such systems, with emphasis on dynamical simulations such as Master-equation evolution [2] and Monte Carlo wave-function simulation [3]. Solution method: Master equation, Monte Carlo wave-function method. Restrictions: Total dimensionality of the system. Master equation – few thousands. Monte Carlo wave-function trajectory – several millions. Unusual features: Because of the heavy use of compile-time algorithms, compilation of programs written in the framework may take a long time and much memory (up to several GBs). Additional comments: The framework is not a program, but provides and implements an application-programming interface for developing simulations in the indicated problem domain. Supplementary information: http://cppqed.sourceforge.net/ . Running time: Depending on the magnitude of the problem, can vary from a few seconds to weeks. References: [1] A. Vukics, H. Ritsch, C++QED: an object-oriented framework for wave-function simulations of cavity QED systems, Eur. Phys. J. D 44 (2007) 585–599. [2] H.J. Carmichael, An Open Systems Approach to Quantum Optics, Springer, 1993. [3] J. Dalibard, Y. Castin, K. Molmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68 (1992) 580.

Cavity cooling of atoms: A quantum statistical treatment

A fully quantum mechanical solution of the dissipative motion of an atomic centre-of-mass strongly coupled to a dynamically varying cavity field mode is presented. Beyond the statistical properties, such as the temperature and localization of the atom, the coherence properties of the atomic wave packet and its entanglement to the cavity field are calculated. The latter is the source of a nonclassical photon statistics expressed in terms of the Mandel Q parameter. The trapping time of an atom initially localized in a potential well is found to significantly deviate from the semiclassically expected results, which we attribute to the graininess of the photon field.