The Carnot limit, formulated in 1824, represents the maximal efficiency of a classical heat engine. In this work we present a thermodynamical analysis of a light amplifier based on a three-level atom coupled off-resonantly to a single quantized cavity mode and to two heat reservoirs with positive temperatures. Based on standard work and heat flow equilibrium, we show that for a cavity blue-detuned with respect to the atomic resonance, the system can surpass the Carnot limit. Nevertheless, the second law of thermodynamics is still obeyed, as the total entropy always increases. By analyzing a semiclassical version of the model, we derive a formula for the critical frequency for which the Carnot limit is broken and a formula for the amplifier efficiency which agrees with its quantum counterpart. In the semiclassical regime, however, the second law is not satisfied and hence it does not offer a physically acceptable description of the system. Finally, we show that breaking the Carnot limit occurs also in a blue-detuned quantum amplifier with output coupling, which represents a realistic model of a laser or maser.

We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e., amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We also describe how this scheme allows one to generate steady-state mechanical entanglement; namely, one can conditionally prepare an entangled, two-mode squeezed mechanical state. This entanglement can be verified directly from the measurement record by applying a generalized version of Duan's inequality; we also discuss how feedback can be used to produce unconditional entanglement.

For nonclassical state generation, we demonstrate the possibility to compensate effects of strong linear loss by engineered nonlinear dissipation. We show that it is always possible to construct such a dissipative gadget that, for a certain class of initial states, the desired nonclassical state can be attained within a particular time interval with an arbitrary precision. Further we demonstrate that an arbitrarily large linear loss can still be compensated by a sufficiently strong coherent or even thermal driving, thus obtaining strongly nonclassical (in particular, sub-Poissonian) stationary mixed states.

We study the modulational instability induced by periodic variations of group-velocity dispersion and nonlinear coefficients in a highly birefringent fiber. We observe, for each resonance order, the presence of two pairs of genuine vector-type sidebands, which are spectrally unbalanced between the polarization components for nonzero group-index mismatch, and one pair of balanced sidebands emerging and dominating at increasing group-index mismatch. As the conventional modulational instability manifests itself, it is partially suppressed by the proximity of these additional unstable regions.

The formation of solitary waves (SW) in media with periodically alternating sign of nonlinearity is investigated under a geometrical phase space approach. It is shown that a remarkably rich set of all types of SW, including bright, dark, antidark, and kink solitons is supported by this type of structure. The existence conditions of all SW are systematically defined in the parameter space of the system and their propagation dynamics are investigated through numerical simulations.

It is known that, in an $(m\otimes n)$-dimensional quantum system, the maximum dimension of a subspace that contains only entangled states is $(m-1)(n-1)$. We show that the exact same bound is tight if we require the stronger condition that every state with range in the subspace has non-positive partial transpose. As an immediate corollary of our result, we solve an open question that asks for the maximum number of negative eigenvalues of the partial transpose of a quantum state. In particular, we give an explicit method of construction of a bipartite state whose partial transpose has $(m-1)(n-1)$ negative eigenvalues, which is necessarily maximal, despite recent numerical evidence that suggested such states may not exist for large $m$ and $n$.

I describe a lattice of asymmetrical qubit pairs in arbitrary dimension, with couplings arranged so that the motion of single-qubit excited states mimics the behavior of charged lattice bosons hopping in a magnetic field. I show, in particular, that one can choose the parameters of the many-body circuit to reach a regime where the complex hopping phase between any two elements can be tuned to any value by simply adjusting the relative phases of two applied oscillating voltage signals. I also propose specific realizations of our model using coupled three junction flux qubits or transmon qubits, in which one can reach the strongly interacting bosonic quantum Hall limit where one will find anyonic excitations. This model could also be studied in trapped ions, and the superconducting circuits could be used for topological quantum computation.

Using linear optical manipulation, single photons, entangled photon pairs, photon measurement, and classical communication, we propose a scheme for a two-spin-qubit phase gate and the teleportation of a controlled-not gate between two electron spins from acting on local qubits to acting on remote qubits using quantum dots in optical microcavities. The scheme is based on spin selective photon reflection from the cavity and is achieved in a deterministic way by the sequential detection of photons and the single-qubit rotations of a single electron spin in a self-assembled GaAs-InAs quantum dot. The feasibility of the scheme is assessed showing that high average fidelities of the gates are achievable in the weak-coupling regime when the side leakage and cavity loss are low. The scheme opens promising possibilities for long-distance quantum communication, distributed quantum computation, and construction of remote quantum-information-processing networks.

We study the quantum error correction threshold of Kitaev's toric code over the group ${\mathbb{Z}}_d$ subject to a generalized bit-flip noise. This problem requires special decoding techniques, and for this purpose we generalize the renormalization-group method we introduced previously [G. Duclos-Cianci and D. Poulin, Phys. Rev. Lett. 104, 050504 (2010) and IEEE Information Theory Workshop, Dublin (2010), p. 1] for ${\mathbb{Z}}_2$ topological codes.

In recent energy loss measurements, band structure effects in electronic stopping have been observed for materials with finite excitation thresholds, for example, noble metals such as Cu and Au. To further investigate the influence of the position of the $d$ band relative to the Fermi edge, electronic stopping of hydrogen and helium ions in Ag and Pt was determined. For Ag, the electronic stopping power exhibits a velocity dependence similar to Cu and Au. No particular effect due to the comparatively large $d$-band offset in Ag is found. In the case of Pt, the electronic stopping power is virtually velocity proportional for H${}^{+}$ ions and exhibits a distinct velocity dependence for He${}^{+}$ ions. For hydrogen the results are compatible with modeling the conduction band as a free electron gas with an energy-dependent effective number of electrons. For He${}^{+}$, however, the observed effects point towards an additional energy loss mechanism, e.g., by charge-exchange processes.

We present a method for the effective preparation of a Bose-Einstein condensate (BEC) into the excited bands of an optical lattice via a standing-wave pulse sequence. With our method, the BEC can be prepared in either a single Bloch state in an excited band or a coherent superposition of states in different bands. Our scheme is experimentally demonstrated by preparing a ${}^{87}$Rb BEC into the $d$ band and the superposition of $s$- and $d$-band states of a one-dimensional optical lattice, within a few tens of microseconds. We further measure the decay of the BEC in the $d$-band state and carry an analytical calculation for the collisional decay of atoms in the excited-band states. Our theoretical and experimental results agree well.

The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and extended to quantum optical polarization. As is shown, this approach properly combines definite time-evolving trajectories with rigorous stationary quantum distributions via the topology displayed by the associated phase field.

By using the close-coupling $R$-matrix method, photodetachment cross sections of negative boron ion are studied. We calculate the electron affinity for the B${}^{-}$(2$s$${}^2$2$p$${}^2$) and find that results agree better with experimental results, after taking into account excitations from 1$s$ shell. We clarify both total photodetachment and partial cross section and discuss its threshold structure. Reasonable agreement of cross section between calculations and experimental data has been achieved.

We analyze the dynamics of dissipative solitons in silicon on insulator waveguides embedded in a gain medium. The optical propagation is modeled through a cubic Ginzburg-Landau equation for the field envelope coupled with an ordinary differential equation accounting for the generation of free carriers owing to two-photon absorption. Our numerical simulations clearly indicate that dissipative solitons accelerate due to the carrier-induced index change and experience a considerable blueshift, which is mainly hampered by the gain dispersion of the active material. Numerical results are fully explained by analytical predictions based on soliton perturbation theory.

We experimentally investigate the effects of noise on the adiabatic and cyclic geometric phase, also termed the Berry phase. By introducing artificial fluctuations in the path of the control field, we measure the geometric contribution to dephasing of an effective two-level system for a variety of noise powers and different paths. Our results, measured using a microwave-driven superconducting qubit, clearly show that only fluctuations which distort the path lead to geometric dephasing. In a direct comparison with the dynamic phase, which is path independent, we observe that the Berry phase is less affected by noise-induced dephasing. This observation directly points towards the potential of geometric phases for quantum gates or metrological applications.

We constructed a virtual quantum computer by running a complete, scaling, quantum-gate–by–quantum-gate implementation of Shor's algorithm on a 128-core classical cluster computer. In mode A [quantum period finding (PF) only, supplied with classical results for the modular exponentiation (ME) part of Shor's algorithm], factoring semiprimes up to $N=557993$ with up to $n=39$ qubits, we confirm earlier, smaller-$n$ results concerning the performance scaling of Shor's algorithm equipped with a truncated (banded) quantum Fourier transform. Running our virtual quantum computer in mode B (full quantum implementation of ME and PF), we find that a large number of gates may be discarded in a scalable way in both the ME and PF parts of Shor's algorithm in exchange for only a small reduction in performance. We explicitly state the associated scaling laws. Implying significant savings in quantum gates, we suggest that these results are of importance for future experimental and technical large-$n$ implementations of quantum computers.

We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. Finally, we study the effect of the detector efficiency on the secret key rate.

We predict a photon Hall effect in the optical cross section of atomic hydrogen, which is caused by the interference between an electric-quadrupole transition and an electric-dipole transition from the ground state to $3D_{3/2}$ and $3P_{3/2}$. This induces a magnetotransverse acceleration comparable to a fraction of $g$.

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-André model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.

We study the conditions for two-photon classical interference with coherent pulses. We find that the temporal overlap between optical pulses is not required for interference. However, coherence within the same inputs is found to be essential for the interference.