arXiv subjects

Sina Khorasani

Publications and source records attributed to Sina Khorasani.

At least 19 recordsLinked to original sources

arXiv2019

Nonlinear Limits to Optomechanical Thermometry

Optomechanical thermometry is a precise and reference-free method to measure absolute temperature. While pumping high optical power is needed to overcome noise and reduce the integration time, there is actually an upper limit to the useful optical power regardless of all other nonideal effects. Side-band inequivalence is a nonlinear effect obtained by higher-order operator algebra in quantum optomechanics and equivalent experiments, which causes asymmetric frequency shifts in side-bands and also an additional difference in their population. This chapter discusses previously unnoticed nonlinear effects arising from side-band inequivalence in optomechanical and Raman thermometry, which determines an upper bound in available optical power for temperature readout.

quant-ph↗

arXiv2019

Operator approach in nonlinear stochastic open quantum physics

The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum optomechanics and quantum computing have a highly nonlinear nature, which makes their analysis extraordinarily difficult using classical schemes. Typically, modern quantum systems of interest nowadays come with four basic properties: (i) quantumness, (ii) openness, (iii) randomness, and (iv) nonlinearity. The newly introduced method of higher-order operators targets analytical solutions to such systems, and while providing at least mathematically approximate expressions with improved accuracy over the fully linearized schemes, some cases admit exact solutions. Many different applications of this method in quantum and classically nonlinear systems are demonstrated throughout. This review is purposed to provide the reader with ease of access to this recent and well-established operator algebra, while going over a moderate amount of literature review. The reader with basic knowledge of quantum mechanics and quantum noise theory should be able to start using this scheme to his or her own problem of interest.

quant-ph↗

arXiv2019

Analysis of Side-band Inequivalence

Frequency shifts of red- and blue-scattered (Stokes/anti-Stokes) side-bands in quantum optomechanics are shown to be counter-intuitively inequal, resulting in an unexpected symmetry breaking. This difference is referred to as Side-band Inequivalenve (SI), which normally leans towards red, and being a nonlinear effect it depends on optical power or intracavity photon number. Also there exists a maximum attainable SI at an optimal operation point. The mathematical method employed here is a combination of operator algebra equipped with harmonic balance, which allows a clear understanding of the associated nonlinear process. This reveals the existence of three distinct operation regimes in terms of pump power, two of which have immeasurably small SI. Compelling evidence from various experiments sharing similar interaction Hamiltonians, including quantum optomechanics, ion/Paul traps, electrooptic modulation, Brillouin scattering, and Raman scattering unambiguously confirm existence of a previously unnoticed SI.

quant-ph↗

arXiv2019

Solution of Cross-Kerr Interaction Combined with Parametric Amplification

We present a full operator approach to treatment of the cross-Kerr interaction combined with parametric amplification. It is shown that this problem can be exactly integrated using the method of higher-order operators. While the initial basis is infinite-dimensional, an orthogonal transformation can reduce the problem exactly into a six-dimensional basis which can be integrated conveniently.

quant-ph↗

arXiv2018

Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms

This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second order operators which constitute an exactly closed commutators. We consider both types of standard position-field and the recently predicted non-standard momentum-field quadratic interactions, which is significant when the ratio of mechanical frequency to optical frequency is not negligible. This unexplored regime of large mechanical frequency can be investigated in few platforms including the superconducting electromechanics and simulating quantum cavity electrodynamic circuits. It has been shown that the existence of non-standard quadratic interaction could be observable under appropriate conditions.

quant-ph↗

arXiv2018

Momentum-Field Interactions Beyond Standard Quadratic Optomechanics

This chapter summarizes the recent progress in the theory and analytical tools of quadratic optomechanical interactions, as one of the prominent domains of contemporary nonlinear quantum optics. Emphasis has been put here first to show what types of nonlinear interactions do exist, and what physical interpretations follow each. The standard quadratic interactions between light and mechanical motion is expressed as the product of cavity light intensity and squared mirror position. However, there exists a non-standard quadratic optomechanical interaction as well, which assumes a mathematically different form and appears as the squared product of field and mirror momenta. This non-standard type of quadratic interaction originates from two corrections: the momentum exchange and conservation among mirror and field, as well as relativistic corrections due to different mechanisms. Both these types of non-standard interactions become relevant when the ratio of mechanical to optical frequency is no longer negligible. Next, we turn to the solution technique of such interactions, and introduce a formal higher-order operator method to tackle the nonlinear evolution of quantum systems. This enables one to accurately study any type of quantum nonlinear interaction using the analysis tools of linear algebra. In order to employ the analytical power of higher-order operator method, one first needs to identify a closed Lie algebra, which should satisfy closedness property under commutation either exactly or approximately, and is referred to as the basis. Having the basis of higher-order operators known, one may proceed to construct the corresponding Langevin equations, which can be now conveniently analyzed using the existing mathematical toolbox of linear algebra to yield the spectral densities, moments, and expectation values.

quant-ph↗

arXiv2018

CUBIT: Capacitive qUantum BIT

In this letter, it is proposed that cryogenic quantum bits can operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated, and the sensitivity of quantum bit frequency and anharmonicity with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process can reveal expected properties, putting the context of quantum computing hardware into new perspectives.

quant-ph↗

arXiv2018

Third-order Optical Nonlinearity in Two-dimensional Transition Metal Dichalcogenides

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer Two-Dimensional (2D) Transition-Metal Dichalcogenides (TMDCs), having the formula $\textrm{MX}_2$ with M=Mo,W and X=S,Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semiclassical perturbation analysis of response functions. We numerically calculate the linear $χ_{μν}^{(1)}(-ω;ω)$ and nonlinear surface susceptibility tensors $χ_{μνζη}^{(3)} (-ω_Σ;ω_r,ω_s,ω_t)$ with $ω_Σ=ω_r+ω_s+ω_t$. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained \textit{with no external fitting parameters} are discussed regarding two recent reported experiments on ${\rm MoS}_2$, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a $\fracπ{4}-$rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and high-harmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

cond-mat.mes-hall↗

arXiv2018

Method of Higher-Order Operators for Quantum Optomechanics

We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises from nonlinear higher-order processes leading to inequal detunings. Similarly, a higher-order resonance shift exists appearing as changes in both of the optical and mechanical resonances. We provide the first known method to explicitly estimate the population of coherent phonons. We also calculate corrections to spring effect due to higher-order interactions and coherent phonons, and show that these corrections can be quite significant in measurement of single-photon optomechanical interaction rate. It is shown that there exists non-unique and various choices for the higher-order operators to solve the optomechanical interaction with different multiplicative noise terms, among which a minimal basis offers exactly linear Langevin equations, while decoupling one Langevin equation and thus leaving the whole standard optomechanical problem exactly solvable by explicit expressions. We finally present a detailed treatment of multiplicative noise as well as nonlinear dynamic stability phases by the method of higher-order operators. Similar approach can be used outside the domain of standard optomechanics to quadratic and all other types of nonlinear interactions in quantum physics.

quant-ph↗

arXiv2017

Electromechanics of Suspended Spiral Capacitors and Inductors

Most electromechanical devices are in two-dimensional metallic drums under high tensile stress, which causes increased mechanical frequency and quality factor. However, high mechanical frequencies lead to small zero-point displacements $x_{\rm zp}$, which limits the single-photon interaction rate $g_0$. For applications which demand large $g_0$, any design with increased $x_{\rm zp}$ is desirable. It is shown that a patterned drum by spiral shape can resolve this difficulty, which is obtained by a reduction of mechanical frequency while the motion mass is kept almost constant. An order of magnitude increase in $g_0$, and agreement between simulations and interferometric measurements is observed.

quant-ph↗

arXiv2017

Higher-order interactions in quantum optomechanics: Analytical solution of nonlinearity

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers, only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches $\sqrt{6}-2$, in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of $Q-$functions, analysis of quantum limited amplifiers, and nondemoliton measurements.

quant-ph↗

arXiv2017

Excitonic emission of monolayer semiconductors near-field coupled to high-Q microresonators

We present quantum yield measurements of single layer $\textrm{WSe}_2$ (1L-$\textrm{WSe}_2$) integrated with high-Q ($Q>10^6$) optical microdisk cavities, using an efficient ($η>$90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe$_2$ to the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ($Q>10^6$) below the bandgap of 1L-WSe$_2$. The nonlinear excitation power dependence of the cavity quantum yield is in agreement with an exciton-exciton annihilation model. The cavity quantum yield is $\textrm{QY}_\textrm{c}\sim10^{-3}$, consistent with operation in the \textit{broad emitter} regime (i.e. the emission lifetime of 1L-WSe$_2$ is significantly shorter than the bare cavity decay time). This scheme can serve as a precise measurement tool for the excitonic emission of layered materials into cavity modes, for both in plane and out of plane excitation.

cond-mat.mes-hall↗

arXiv2017

Optical wave evolution due to interaction with elastic wave in a phoxonic crystal slab waveguide

Phoxonic crystal as a means of guiding and confining electromagnetic and elastic waves has already attracted attentions. Lack of exact knowledge on how these two types of waves interact inside this crystal and how electromagnetic wave evolves through this interaction has increased this field complexity. Here we explain how an elastic wave affects an electromagnetic wave through photo-elasticity and interface displacement mechanisms in a phoxonic crystal slab waveguide. We obtain a master equation which can describe electromagnetic wave evolution. In this equation we define a coupling parameter and calculate its value for different modes of electromagnetic and elastic waves and show it vanishes for some types of modes . Finally we solve the master equation for a typical phoxonic crystal slab waveguide and illustrate the electromagnetic wave evolution.

physics.optics↗

arXiv2017

Efficient Analysis of Confined Guided Modes in Phoxonic Crystal Slabs

Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic and phononic (phoxonic) crystals in full three dimensions is not suitable for slab analysis in its standard form, because of convergence and stability issues. Here, we propose a modification to this method which overcomes these limitations. This improved method can be utilized for calculation of both photonic and phononic modes in phoxonic slabs. While in the standard three-dimensional PWE, Fourier series are used to estimate the field dependence across the normal component of the slab, we expand the fields across the third dimension using eigenmodes of a plain unstructured slab. Despite its approximate nature, this approach is observed to be both much faster and more accurate than the conventional PWE method and can give a very accurate estimation of confined propagating modes. As an application example of the proposed method we investigate a non-reciprocal photonic device. This device is a phoxonic slab waveguide which changes modes of optical waves by elastic waves and can be used as an optical insulator or mode converter.

physics.optics↗

arXiv2017

Higher-order interactions in quantum optomechanics: Revisiting theoretical foundations

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in previous studies. Corrections to the quadratic terms are particularly significant when the mechanical frequency is of the same order or larger than the electromagnetic frequency. Further discussions on the squeezing as well as relativistic corrections are presented.

quant-ph↗

arXiv2017

Diamond Configuration for Non-reciprocal Transmission

A system scheme is presented which allows non-reciprocal wave transmission or directional amplification of electromagnetic signals, using a boxed four-node method. Edges represent strong hopping interactions and diagonals stand for weak parametric interactions. Using careful optimization of values for design parameters, we are able to obtain non-reciprocity in excess of 12dB and 130dB for intrinsic and extrinsic configurations at identical input/output frequencies. For the directional amplification, an isolation as high as 40dB is demonstrated with forward/backward gains of $\pm$20dB. Cascading two such systems potentially can offer high isolations at high gains.

quant-ph↗

arXiv2017

Time Operator in Relativistic Quantum Mechanics

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint $4\times 4$ relativistic time operator for spin-$\frac{1}{2}$ particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

quant-ph↗

arXiv2017

Nonlinear Graphene Quantum Capacitors for Electro-optics

Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride respectively as the electrodes and the insulating dielectric, a strongly nonlinear behavior at zero bias and small voltages is obtained. When the temperature is sufficiently low, the strong nonlinear interaction emerging from the quantum capacitance exhibits a diverse range of phenomena. The proposed structure could take over the functionalities of nonlinear elements in many cryogenic quantum systems, and in particular, quantum electro-optics. It is shown that ultrastrong coupling is easily reached with small number of pump photons at temperatures around 1K and capacitor areas of the order of $1μ{\textrm{m}}^2$. A measure of anharmonicity is defined and as potential applications, a qubit design as well as schemes for non-reciprocal devices such as an electromagnetic frequency circulator are discussed.

quant-ph↗