arXiv subjects

Hakan E. Tureci

Publications and source records attributed to Hakan E. Tureci.

At least 19 recordsLinked to original sources

arXiv2017

Spatial correlations in driven-dissipative photonic lattices

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose-Hubbard and spin-$1/2$ XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array ($\sim 1/z$) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) We show that the gas--liquid transition in the driven-dissipative Bose-Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching--bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-$1/2$ XY model and provide a simple explanation of this phenomenon.

cond-mat.stat-mech↗

arXiv2016

Stable Switching among High-Order Modes in Polariton Condensates

We report multistate optical switching among high-order bouncing-ball modes ("ripples") and whispering-gallerying modes ("petals") of exciton-polariton condensates in a laser-generated annular trap. By tailoring the diameter and power of the annular trap, the polariton condensate can be switched among different trapped modes, accompanied by redistribution of spatial densities and superlinear increase in the emission intensities, implying that polariton condensates in this geometry could be exploited for a multistate switch. A model based on non-Hermitian modes of the generalized Gross-Pitaevskii equation reveals that this mode switching arises from competition between pump-induced gain and in-plane polariton loss. The parameters for reproducible switching among trapped modes have been measured experimentally, giving us a phase diagram for mode switching. Taken together, the experimental result and theoretical modeling advances our fundamental understanding of the spontaneous emergence of coherence and move us toward its practical exploitation.

cond-mat.mes-hall↗

arXiv2016

Interaction-induced mode switching in steady-state microlasers

We demonstrate that due to strong modal interactions through cross-gain saturation, the onset of a new lasing mode can switch off an existing mode via a negative power slope. In this process of interaction-induced mode switching (IMS) the two involved modes maintain their identities, i.e. they do not change their spatial field patterns or lasing frequencies. For a fixed pump profile, a simple analytic criterion for the occurrence of IMS is given in terms of their self- and cross-interaction coefficients and non-interacting thresholds, which is verified for the example of a two-dimensional microdisk laser. When the spatial pump profile is varied as the pump power is increased, IMS can be induced even when it would not occur with a fixed pump profile, as we show for two coupled laser cavities. Our findings apply to steady-state lasing and are hence different from dynamical mode switching or hopping. IMS may have potential applications in robust and flexible all-optical switching.

physics.optics↗

arXiv2015

Origin and Implications of $A^2$-like Contribution in the Quantization of Circuit-QED Systems

By placing an atom into a cavity, the electromagnetic mode structure of the cavity is modified. In Cavity QED, one manifestation of this phenomenon is the appearance of a gauge-dependent diamagnetic term, known as the $A^2$ contribution. Although in atomic Cavity QED, the resulting modification in the eigenmodes is negligible, in recent superconducting circuit realizations, such corrections can be observable and may have qualitative implications. We revisit the canonical quantization procedure of a circuit QED system consisting of a single superconducting transmon qubit coupled to a multimode superconducting microwave resonator. A complete derivation of the quantum Hamiltonian of an open circuit QED system consisting of a transmon qubit coupled to a leaky transmission line cavity is presented. We introduce a complete set of modes that properly conserves the current in the entire structure and present a sum rule for the dipole transition matrix elements of a multi-level transmon qubit coupled to a multi-mode cavity. Finally, an effective multi-mode Rabi model is derived with coefficients that are given in terms of circuit parameters.

cond-mat.mes-hall↗

arXiv2015

Inverse Vernier Effects in Coupled Lasers

In this report we study the Vernier effect in coupled laser systems consisting of two cavities. We show that depending on the nature of their coupling, not only can the "supermodes" formed at the overlapping resonances of the coupled cavities have the lowest thresholds and lase first as previously suggested, leading to a manifestation of the typical Vernier effect now in an active system; these supermodes can also have increased thresholds and are hence suppressed, which can be viewed as an inverse Vernier effect. We attribute this effect to detuning-dependent Q-spoiling, and it can lead to an increased free spectrum range and possibly single-mode lasing, which may explain the experimental findings of several previous work. We illustrate this effect using two coupled micro-ring cavities and a micro-ring cavity coupled to a slab cavity, and we discuss its relation to the existence of exceptional points in coupled lasers.

physics.optics↗

arXiv2015

Beyond Strong Coupling in a Massively Multimode Cavity

The study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED). The achievement of strong coupling, where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations. Here we introduce multimode strong coupling (MMSC), where the coupling is comparable to the free spectral range (FSR) of the cavity, i.e. the rate at which a qubit can absorb a photon from the cavity is comparable to the round trip transit rate of a photon in the cavity. We realize, via the circuit QED architecture, the first experiment accessing the MMSC regime, and report remarkably widespread and structured resonance fluorescence, whose origin extends beyond cavity enhancement of sidebands. Our results capture complex multimode, multiphoton processes, and the emergence of ultranarrow linewidths. Beyond the novel phenomena presented here, MMSC opens a major new direction in the exploration of light-matter interactions.

quant-ph↗

arXiv2014

Anomalous transient amplification of waves in non-normal photonic media

Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally been the mitigation of optical losses. Recent work has shown that a new class of optical materials that consist of a precisely balanced distribution of loss and gain can be exploited to engineer novel functionalities for propagating and filtering electromagnetic radiation. Here we show a generic property of optical systems that feature an unbalanced distribution of loss and gain, described by non-normal operators, namely that an overall lossy optical system can transiently amplify certain input signals by several orders of magnitude. We present a mathematical framework to analyze the dynamics of wave propagation in media with an arbitrary distribution of loss and gain and construct the initial conditions to engineer such non-normal power amplifiers. Our results point to a new design space for engineered optical systems employed in photonics and quantum optics.

physics.optics↗

arXiv2014

Enhancement of Laser Power Efficiency by Control of Spatial Hole Burning Interactions

The laser is an out-of-equilibrium nonlinear wave system where the interplay of the cavity geometry and nonlinear wave interactions, mediated by the gain medium, determines the self-organized oscillation frequencies and the associated spatial field patterns. In the steady state, a constant energy flux flows through the laser from the pump to the far field, with the ratio of the total output power to the input power determining the power-efficiency. While nonlinear wave interactions have been modeled and well understood since the early days of laser theory, their impact on the power-efficiency of a laser system is poorly understood. Here, we show that spatial hole burning interactions generally decrease the power efficiency. We then demonstrate how spatial hole burning interactions can be controlled by a spatially tailored pump profile, thereby boosting the power-efficiency, in some cases by orders of magnitude.

physics.optics↗

arXiv2014

Route from spontaneous decay to complex multimode dynamics in cavity QED

We study the non-Markovian quantum dynamics of an emitter inside an open multimode cavity, focusing on the case where the emitter is resonant with high-frequency cavity modes. Based on a Green's function technique suited for open photonic structures, we study the crossovers between three distinct regimes as the coupling strength is gradually increased: (i) overdamped decay with a time scale given by the Purcell modified decay rate, (ii) underdamped oscillations with a time scale given by the effective vacuum Rabi frequency, and (iii) pulsed revivals. The final multimode strong coupling regime (iii) gives rise to quantum revivals of the atomic inversion on a time scale associated with the cavity round-trip time. We show that the crucial parameter to capture the crossovers between these regimes is the nonlinear Lamb shift, accounted for exactly in our formalism.

quant-ph↗

arXiv2013

Pattern Formation and Strong Nonlinear Interactions in Exciton-Polariton Condensates

Exciton-polaritons generated by light-induced potentials can spontaneously condense into macroscopic quantum states that display nontrivial spatial and temporal density modulation. While these patterns and their dynamics can be reproduced through the solution of the generalized Gross-Pitaevskii equation, a predictive theory of their thresholds, oscillation frequencies, and multi-pattern interactions has so far been lacking. Here we represent such an approach based on the linear non-Hermitian modes of the complex-valued light-induced potential. We provide a simple analytic expression for the lowest thresholds that is able to explain the modal patterns observed in recent experiments for various pump geometries. We also show that the evolution of the condensate with increasing pump strength is strongly geometry dependent and can display contrasting features such as enhancement or reduction of the spatial localization of the condensate.

cond-mat.mes-hall↗

arXiv2013

Gain-tunable optomechanical cooling in a laser cavity

We study the optical cooling of the resonator mirror in a cavity-optomechanical system that contains an optical gain medium. We find that the optical damping rate is vanishingly small for an incoherently pumped laser above threshold. In the presence of an external coherent drive however, the optical damping rate can be enhanced substantially with respect to that of a passive cavity. We show that the strength of the incoherent pump provides a conduit to tune the damping rate and the minimum attainable phonon number with the same radiation pressure force, and the latter can be lowered from that of a passive cavity if the thermal contribution is nonnegligible. We also show that the system can undergo a transition from the weak optomechanical coupling regime to the strong optomechanical coupling regime as the incoherent pump strength is varied.

quant-ph↗

arXiv2008

The quantum optical Josephson interferometer

The interplay between coherent tunnel coupling and on-site interactions in dissipation-free bosonic systems has lead to many spectacular observations, ranging from the demonstration of number-phase uncertainty relation to quantum phase transitions. To explore the effect of dissipation and coherent drive on tunnel coupled interacting bosonic systems, we propose a device that is the quantum optical analog of a Josephson interferometer. It consists of two coherently driven linear optical cavities connected via a central cavity with a single-photon nonlinearity. The Josephson-like oscillations in the light emitted from the central cavity as a function of the phase difference between two pumping fields can be suppressed by increasing the strength of the nonlinear coupling. Remarkably, we find that in the limit of ultra-strong interactions in the center-cavity, the coupled system maps on to an effective Jaynes-Cummings system with a nonlinearity determined by the tunnel coupling strength. In the limit of a single nonlinear cavity coupled to two linear waveguides, the degree of photon antibunching from the nonlinear cavity provides an excellent measure of the transition to the nonlinear regime where Josephson oscillations are suppressed.

cond-mat.mes-hall↗

arXiv2007

An efficient Fredholm method for calculation of highly excited states of billiards

A numerically efficient Fredholm formulation of the billiard problem is presented. The standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first. We next reformulate the singularity condition in terms of a flow in the space of an auxiliary one-parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain. Based on this analytic behavior we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations.

nlin.CD↗

arXiv2007

Strong Electron-Hole Exchange in Coherently Coupled Quantum Dots

We have investigated few-body states in vertically stacked quantum dots. Due to small inter-dot tunneling rate, the coupling in our system is in a previously unexplored regime where electron-hole exchange is the dominant spin interaction. By tuning the gate bias, we are able to turn this coupling off and study a complementary regime where total electron spin is a good quantum number. The use of differential transmission allows us to obtain unambiguous signatures of the interplay between electron and hole spin interactions. Small tunnel coupling also enables us to demonstrate all-optical charge sensing, where conditional exciton energy shift in one dot identifies the charging state of the coupled partner.

cond-mat.mes-hall↗

arXiv2006

Ray-wave correspondence in the nonlinear description of stadium-cavity lasers

We show that the solution of fully nonlinear lasing equations for stadium cavities exhibits a highly directional emission pattern. This directionality can be well explained by a ray-dynamical model, where the dominant ray-escape dynamics is governed by the unstable manifolds of the unstable short periodic orbits for the stadium cavity. Investigating the cold-cavity modes relevant for the lasing, we found that all of the high-Q modes have the emission directionality corresponding to that of the ray-dynamical model.

physics.optics↗

arXiv2006

Self-consistent multi-mode lasing theory for complex or random lasing media

A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing modes, we introduce an appropriate discrete basis of functions which describe also the intensity and angular emission pattern outside the cavity. This constant flux (CF) basis is dictated by the Green function which arises when formulating the steady state Maxwell-Bloch equations as a self-consistent linear response problem. This basis is similar to the quasi-bound state basis which is familiar in resonator theory and it obeys biorthogonality relations with a set of dual functions. Within a single-pole approximation for the Green function the lasing modes are proportional to these CF states and their intensities and lasing frequencies are determined by a set of non-linear equations. When a near threshold approximation is made to these equations a generalized version of the Haken-Sauermann equations for multi-mode lasing is obtained, appropriate for open cavities. Illustrative results from these equations are given for single and few mode lasing states, for the case of dielectric cavity lasers. The standard near threshold approximation is found to be unreliable. Applications to wave-chaotic cavities and random lasers are discussed.

cond-mat.mes-hall↗

arXiv2006

Spin-orbit interaction in quantum dots in the presence of exchange correlations

We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different symmetries of the spin-orbit coupling, the problem has no closed solution. A conventional choice of a many-particle basis in a numerical diagonalization is the set of Slater determinants built from the single-particle eigenstates of the one-body Hamiltonian (including the spin-orbit terms). We develop a different approach based on the use of a good-spin many-particle basis that is composed of the eigenstates of the universal Hamiltonian in the absence of spin-orbit scattering. We introduce a complete labelling of this good-spin basis and use angular momentum algebra to calculate in closed form the matrix elements of the spin-orbit interaction in this basis. Spin properties, such as the ground-state spin distribution and the spin excitation function, are easily calculated in this basis.

cond-mat.mes-hall↗

arXiv2005

Polarization properties and dispersion relations for spiral resonances of a dielectric rod

Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obtained using the eikonal (Einstein-Brillouin-Keller) method which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far-field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.

physics.optics↗