The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general (m-1)-th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of (m-1)-th order nonlinear medium.
The coherent evolution of two atomic qubits mediated by a set of bosonic field modes is investigated. By assuming a specific encoding of the quantum states in the internal levels of the two atoms we show that entangling quantum gates can be realised, with high fidelity, even when a large number of mediating modes is involved. The effect of losses and imperfections on the gates' operation is also considered in detail.
We propose and analyze a scheme for "on demand" creation of coherent superposition of meta-stable states in a tripod-structured atom using frequency-chirped laser pulses. Negligible excitation of the atoms during the creation of the superposition states is a priority in our consideration. The underlying physics of the scheme is explained using the formalism of adiabatic states. By numerically solving master equation for the density matrix operator, we analyze the influence of the spontaneous decay and transverse relaxation on the efficiency of the creation of superposition states. We show that…
Coherent diffusion pertains to the motion of atomic dipoles experiencing frequent collisions in vapor while maintaining their coherence. Recent theoretical and experimental studies on the effect of coherent diffusion on key Raman processes, namely Raman spectroscopy, slow polariton propagation, and stored light, are reviewed in this Colloquium.
Models of universal quantum computation in which the required interactions between register (computational) qubits are mediated by some ancillary system are highly relevant to experimental realisations of a quantum computer. We introduce such a universal model that employs a $d$-dimensional ancillary qudit. The ancilla-register interactions take the form of controlled displacements operators, with a displacement operator defined on the periodic and discrete lattice phase space of a qudit. We show that these interactions can implement controlled phase gates on the register by utilising geometri…
Quantum simulators employing cold atoms are among the most promising approaches to tackle quantum many-body problems. Nanophotonic structures are widely employed to engineer the bandstructure of light and are thus investigated as a means to tune the interactions between atoms placed in their vicinity. A key shortcoming of this approach is that excitations can decay into free photons, limiting the coherence of such quantum simulators. Here, we overcome this challenge by proposing to use a simple cubic three-dimensional array of atoms to produce an omnidirectional bandgap for light and show that…
We investigate the coherent energy transfer between two quantum systems mediated by a quantum bus. In particular, we consider the energy transfer process between two qubits, and how it can be influenced by using a third qubit or photons in a resonant cavity as mediators. Inspecting different figures of merit and considering both on and off-resonance configurations, we characterize the energy transfer performances. We show that, while the qubit-mediated transfer shows no advantages with respect to a direct coupling case, the cavity-mediated one is progressively more and more efficient as functi…
Scalable architectures for quantum information technologies require to selectively couple long-distance qubits while suppressing environmental noise and cross-talk. In semiconductor materials, the coherent coupling of a single spin on a quantum dot to a cavity hosting fermionic modes offers a new solution to this technological challenge. Here, we demonstrate coherent coupling between two spatially separated quantum dots using an electronic cavity design that takes advantage of whispering-gallery modes in a two-dimensional electron gas. The cavity-mediated long-distance coupling effectively min…
We consider transfer of optical vortices between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by the $Λ$ configuration of the atom-light coupling. The atoms are initially prepared in a coherent superposition of the lower levels, creating a so-called phaseonium medium. If a single vortex beam initially acts on one transition of the $Λ$ scheme, an extra laser beam is subsequently generated with the same vorticity as that of the incident vortex beam. The absorption of the incident probe beam takes place mostly at the beginning of the atomic medium wi…
Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent/incoherent driving for the case of two coupled cavity-QED systems. We discuss qualitative differences between these excitations scenarios, which are particular strong for higher-order photon-photon correlations: $g^{(n)}(0)$ with $ n>2 $. Quantum cascaded systems show a behavior differing from the idealized cases of individual coherent/incoherent driving and allow to produce qualitatively d…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition to the nonlinear Schroedinger equation, important examples include the derivative nonlinear Schroedinger equation, the quintic complex Ginzburg-Landau equation, and the Gerdjikov-Ivanov equation. This approach provides a mathematical description of nonstationary media supporting unidimensional signal propagation and/or total field trapping. In particular, we …
Spin-orbit coupling of optical vector vortices in coherently prepared media
Institute of Theoretical Physics and Astronomy, Vilnius University（维尔纽斯大学理论物理与天文研究所）；Laser Research Center, Vilnius University（维尔纽斯大学激光研究中心）；Département Physique, Faculté des Sciences, Aix-Marseille Université（艾克斯-马赛大学理学院物理系）；Baltic Institute of Advanced Technology（波罗的海高级技术研究所）
Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, restricting the range of the coupling to small distances. We use a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of one meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, …
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeabil…
We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described …
We study theoretically how multiple scattering of light in a disordered medium can spontaneously generate quantum correlations. In particular we focus on the case where the input state is Gaussian and characterize the correlations between two arbitrary output modes. As there is not a single all-inclusive measure of correlation, we characterise the output correlations with three measures: intensity fluctuations, entanglement, and quantum discord. We found that, while a single mode coherent state input can not produce quantum correlations, any other Gaussian input will produce them in one form o…
Beam splitter mediated entanglement of nonlinear photon-added coherent states was studied by Honarasa, Bagheri and Gharaati [1]. We believe that this work contains errors in numerical computations of linear entropy and Mandel parameter which lead to wrong conclusions. We point out the possible errors and describe the necessary corrections. The conclusions based on our arguments are in complete agreement with previously published literature.
We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around $g_s/2π= 40 \ \text{MHz}$. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around $2J/2π= 20 \ \text{MHz}$. In addition, photon-number states are resolved from the shift $2χ_s/2π= -13 \ \text{MHz}$ that they induce on the s…
Coherent nonlinear multi-pulse processes, nonlinear waves and echo effects in resonant media are the topical problems of modern optics and important tools of coherent spectroscopy and quantum information science. We generalize the McCall-Hahn area theorem to the formation of an arbitrary photon echo generated during the multi-pulse excitation of the optically dense resonant media. The derived theorem made it possible to reveal the nonlinear mechanism of generation and evolution of the photon echo signals inside the media after a two-pulse excitation. We find that a series of self-reviving echo…
Long-range coherent interactions between quantum emitters are instrumental for quantum information and simulation technologies, but they are generally difficult to isolate from dissipation. Here, we show how such interactions can be obtained in photonic Weyl environments due to the emergence of an exotic bound state whose wavefunction displays power-law spatial confinement. Using an exact formalism, we show how this bound state can mediate coherent transfer of excitations between emitters, with virtually no dissipation and with a transfer rate that follows the same scaling with distance as the…
We address a fundamental question of quantum optics: Can a beam of light mediate coherent Hamiltonian interactions between two distant quantum systems? This is an intriguing question whose answer is not a priori clear, since the light carries away information about the systems and might be subject to losses, giving rise to intrinsic decoherence channels associated with the coupling. Our answer is affirmative and we derive a particularly simple sufficient condition for the interactions to be Hamiltonian: The light field needs to interact twice with the systems and the second interaction has to …
Entangling gates for electron spins in semiconductor quantum dots are generally based on exchange, a short-ranged interaction that requires wavefunction overlap. Coherent spin-photon coupling raises the prospect of using photons as long-distance interconnects for spin qubits. Realizing a key milestone for spin-based quantum information processing, we demonstrate microwave-mediated spin-spin interactions between two electrons that are physically separated by more than 4 mm. Coherent spin-photon coupling is demonstrated for each individual spin using microwave transmission spectroscopy. An enhan…
Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle, which represents a significant constraint towards scaling to reach dense 1D or 2D arrays of QD qubits. Following the success of circuit quantum eletrodynamics [6], …
Optical networks that distribute entanglement among quantum technologies will form a powerful backbone for quantum science but are yet to interface with leading quantum hardware such as superconducting qubits. Consequently, these systems remain isolated because microwave links at room temperature are noisy and lossy. Building connectivity requires interfaces that map quantum information between microwave and optical fields. While preliminary microwave-to-optical (M2O) transducers have been realized, developing efficient, low-noise devices that match superconducting qubit frequencies (gigahertz…
The purpose of this paper is to present a comprehensive study of a coherent feedback network where the main component consists of two distant double quantum dot (DQD) qubits which are directly coupled to a cavity. This main component has recently been physically realized (van Woerkom, {\it et al.}, Microwave photon-mediated interactions between semiconductor qubits, Physical Review X, 8(4):041018, 2018). The feedback loop is closed by cascading this main component with a beamsplitter. The dynamics of this coherent feedback network is studied from three perspectives. First, an analytic form of …
A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in nonlinear Kerr media and an extended phase space evolution equation is derived along with invariant quantities. We further consider modulation instability as well as the extension to partially coherent fields.
