## Maciej Maśka

RECENT COLLABORATIONS

- N. Trivedi (Ohio State University, Columbus, USA)
- C. Clark, Join Quantum Institute, College Park, USA)
- M. Mierzejewski (Univ. of Silesia, Katowice)
- E. Kochetov (JINR, Dubna)
- A. Ferraz (Univ. de Brasilia, Brasilia)
- J. Freericks (Georgetown Univ. , Washington DC, USA)
- R. Lemański (PAS, Wrocław)
- C. Williams, P. Julienne, T. Hanna (NIST, Geithsburg, USA)
- A. Hu, (Univ. of Maryland, College Park) (⇒ in Polish)
- R. J. Cava, T. Klimczuk, M. L. Foo (Princeton Univ., Princeton, USA)
- T. Domański (UMCS, Lublin)
- B. Andrzejewski (PAS, Poznań)
- J. Sadowski (MAX-Lab, Lund Univ., PAS, Warszawa)
- J. Spalek (Jagiellonian Univ., Krakow)
- J. Bonca, L. Vidmar (University of Ljubljana)
- O. P. Sushkov (University of New South Wales, Syndey, Australia)

**RECENT RESEARCH**

**COLD ATOMS IN OPTICAL LATTICES**

- Ultracold atoms trapped in optical lattices are providing a new laboratory to study quantum phases of many-body condensed matter systems. It has already been demonstrated that strong correlations in cold atom systems can lead to the Mott transition. The next step would be to show that these systems can "mimic" also magnetic phases. Some recent experiments indicate that there is a progress in these attempts, but the problem is that the lowest experimentally accessible temperature is still larger than the critical temperature. One way to tackle this problem is to develop new efficient cooling techniques. We, however, propose another approach, namely we suggest to use a system with higher critical temperature. Using the Monte Carlo and Dynamical Mean Field Theory we show that the temperature of the transition to a checkerboard phase (an analog to the Neels state) in the Falicov-Kimball model increases almost linerly with the number of spin states of the light atoms. Therefore, we propose to perform an experiment in mixtures of high-spin light (mobile) and heavy (localized) atoms and properly chosing the elements we would be able to observe the magnetic state within the experimentally accessible regime.

(in collaboration with J. Freerics) - We consider a coupled boson-fermion model in two dimensions, that describes itinerant fermions hybridizing with localized bosons composed of pairs of tightly bound opposite–spin fermions. We trace out the fermionic degrees of freedom and perform a Monte Carlo simulation for the effective classical Hamiltonian of boson phases. We find that the fermions not only generate an effective long-range temperature-dependent boson-boson coupling that generates a finite phase stiffness, but remarkably the phase stiffness is considerably more robust than that described by the XY model. Our analysis further shows that the fermion-boson hybridization leads to an effective long-range temperature-dependent interaction between the boson phases, with inter-vortex interaction in the effective model that is a power law rather than logarithmic as in the XY model.

(in collaboration with N. Trivedi) - Ultracold mixtures of different atomic species have great promise for realizing novel many-body phenomena. In a binary mixture of femions with a large mass difference and repulsive interspecies interactions, a disordered Mott insulator phase can occur. This phase displays an incompressible total density, although the relative density remain compressible. We use strong-coupling and Monte Carlo calculations to show that this phase exists for a broad parameter region for ultracold gases confined in a harmonic trap on a three-dimensional optical lattice, for experimentally accessible values of the trap parameters.

(Anzi Hu, M. M. Maśka, Charles W. Clark, J. K. Freericks, "Robust finite-temperature disordered Mott insulating phases in inhomogeneous Fermi-Fermi mixtures with density and mass imbalance", arXiv:1407.100) - The momentum distribution is one of the most important quantities which provides information about interactions in many-body systems. At the same time it is a quantity that can easily be accessed in experiments on ultracold atoms. In this paper, we consider mixtures of light- and heavy-fermionic atoms in an optical lattice described effectively by the Falicov-Kimball model. Using a Monte Carlo method, we study how different ordered density-wave phases can be detected by measurement of the momentum distribution of the light atoms. We also demonstrate that ordered phases can be seen in Bragg scattering experiments. Our results indicate that the main factor that determines the momentum distribution of the light atoms is the trap confinement. On the other hand, the pattern formed by the heavy atoms seen in the Bragg scattering experiments is very sensitive to the temperature and possibly can be used in low-temperature thermometry.

(M. M. Maśka, R. Lemański, C. J. Williams, and J. K. Freericks, "Momentum distribution and ordering in mixtures of ultracold light- and heavy-fermion atoms", Phys. Rev. A 83, 063631 (2011)) - We discuss the application of a strong-coupling expansion (perturbation theory in the hopping) for studying light-Fermi–heavy-Bose (like K
^{40}-Rb^{87}) mixtures in optical lattices. We use the strong-coupling method to evaluate the efficiency for preforming molecules, the entropy per particle, and the thermal fluctuations. We show that within the strong interaction regime (and at high temperature), the strong-coupling expansion is an economical way to study this problem. In some cases, it remains valid even down to low temperatures. Because the computational effort is minimal, the strong-coupling approach allows us to work with much larger system sizes, where boundary effects can be eliminated, which is particularly important at higher temperatures. Since the strong-coupling approach is so efficient and accurate, it allows one to rapidly scan through parameter space in order to optimize the preforming of molecules on a lattice (by choosing the lattice depth and interspecies attraction). Based on the strong-coupling calculations, we test the thermometry scheme based on the fluctuation-dissipation theorem and find the scheme gives accurate temperature estimation even at very low temperature. We believe this approach and the calculation results will be useful in the design of the next generation of experiments and will hopefully lead to the ability to form dipolar matter in the quantum degenerate regime.

(Anzi Hu, J. K. Freericks, M. M. Maśka, and C. J. Williams, Efficiency for preforming molecules from mixtures of light Fermi and heavy Bose atoms in optical lattices: The strong-coupling-expansion method, Phys. Rev. A 83, 043617 (2011)) - J.K. Freericks, M.M. Maska, Anzi Hu, T.M. Hanna, C.J. Williams, P.S. Julienne, and R. Lemanski,"Improving the efficiency of ultracold dipolar molecule formation by first loading onto an optical lattice", Phys. Rev. A 81, 011605(R) (2010)
- M.M. Maska, R. Lemanski, J.K. Freericks, and C.J. Williams, "Pattern formation in mixtures of ultracold atoms in optical lattices", Phys. Rev. Lett. 101, 060404 (2008)

**NANOPHYSICS**

- Transport properties of a gated nanostructure depend crucially on the coupling of its states to the states of electrodes. In the case of a single quantum dot the coupling, for a given quantum state, is constant or can be slightly modified by additional gating. In this paper we consider a concentric dot–ring nanostructure (DRN) and show that its transport properties can be drastically modified due to the unique geometry. We calculate the dc current through a DRN in the Coulomb blockade regime and show that it can efficiently work as a single electron transistor or a current rectifier. In both cases the transport characteristics strongly depends on the details of the confinement potential. The calculations are done for low and high bias regime, the latter being especially interesting in the context of current rectification due to fast relaxation processes.
- Modern nanotechnology allows the production of, depending on the application, various quantum nanostructures with selected properties. These properties are strongly influenced by the confinement potential which can be modified e.g. by electrical gating. In this paper, we analyze a nanostructure composed of a quantum dot surrounded by a quantum ring. We show that, depending on the details of the confining potential, the electron wave functions can be located in different parts of the structure. Since many properties of such a nanostructure strongly depend on the distribution of the wave functions, by varying the applied gate voltage one can easily control them. In particular, we illustrate the high controllability of the nanostructure by demonstrating how its coherent, optical and conducting properties can be drastically changed by a small modification of the confining potential.

(E. Zipper, M. Kurpas, M.M. Maska, "Wave function engineering in quantum dot-ring nanostructures", New Journal of Physics 14, 093029 (2012))

**CONDENSED MATTER PHYSICS**

- The hydrogen molecules
*H*and (_{2}*H*)_{2}are analyzed with electronic correlations taken into account between the_{2}*1s*electrons in an exact manner. The optimal single-particle Slater orbitals are evaluated in the correlated state of*H*by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron–ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for the 2x(_{2}*H*)_{2}rectangular configuration, as well its ground state energy._{2}

(A.P. Kadzielawa, A. Bielas, M. Acquarone, A. Biborski, M.M. Maska, J. Spalek, "H2 and (H2)2 molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters", New J. Phys. 16, 123022 (2014)) - We report the electric transport and thermodynamic properties of the skutterudite-related La
_{3}Co_{4}Sn_{13}and La_{3}Rh_{4}Sn_{13}superconductors. Applying an external pressure to La_{3}Rh_{4}Sn_{13}, the resistive superconducting critical temperature Tc decreases, while the critical temperature of La_{3}Co_{4}Sn_{13}is enhanced with increasing pressure. The positive pressure coefficient dTc/dP correlates with a subtle structural transition in La_{3}Co_{4}Sn_{13}and is discussed in the context of lattice instabilities. Specific-heat data show that both compounds are typical BCS superconductors. However, La_{3}Rh_{4}Sn_{13}also exhibits a second superconducting phase at higher temperatures, which is characteristic of inhomogeneous superconductors. We calculate the specific heat for an inhomogeneous superconducting phase, which agrees well with experimental C(T) data for La_{3}Rh_{4}Sn_{13}. We also found that an applied pressure reduces this second superconducting phase.

(A. Slebarski, M. Fijałkowski, M. M. Maska, M. Mierzejewski, B. D. White, and M. B. Maple, "Superconductivity of La_{3}Co_{4}Sn_{13}and La_{3}Rh_{4}Sn_{13}: A comparative study", Phys. Rev. B 89, 12511 (2014)) - The
*t–J*model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.

(M.M. Maska, M. Mierzejewski, E. Kochetov, "The Ising version of the t–J model", Philosophical Magazine 2014)