arXiv subjects

J. E. Sipe

Publications and source records attributed to J. E. Sipe.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum-Referenced Spontaneous Emission Tomography

We present a method of tomography that measures the joint spectral phase (JSP) of spontaneously emitted photon pairs originating from a largely uncharacterized ``target" source. We use quantum interference between our target source and a reference source to extract the JSP with four spectrally resolved measurements, in a process that we call quantum-referenced spontaneous emission tomography (Q-SpET). We have demonstrated this method on a photonic integrated circuit for a target micro-ring resonator photon-pair source. Our results show that spontaneously emitted photon pairs from a micro-ring resonator are distinctively different from that of stimulated emission, and thus cannot in general be fully characterized using classical stimulated emission tomography without detailed knowledge of the source.

quant-ph↗

arXiv2023

Taking apart squeezed light

We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to "take apart" the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.

quant-ph↗

arXiv2023

Proof of Gauge-Invariance of Magnetic Susceptibility of Topologically Trivial Insulators in the Independent Particle Approximation

We have derived an expression for the magnetic susceptibility of topologically trivial insulators, however an important consideration for any response tensor is whether it is gauge-invariant. By this we refer to the gauge-freedom in choosing the Bloch functions one uses in a computation since multiplication by an arbitrary $\textbf{k}$-dependent complex phase produces equally valid Bloch functions. Additionally Wannier functions, which can be constructed by a unitary mixing of the Bloch functions, are a useful basis for computation due to their localized properties, but are strongly non-unique. Therefore, we show that the theoretical expression we derived is independent of the choice of Bloch functions or Wannier functions used, and thus is gauge-invariant in this sense.

cond-mat.mes-hall↗

arXiv2023

Microscopic Theory of the Magnetic Susceptibility of Insulators

We present a general theory of the magnetic susceptibility of insulators that can be extended to treat spatially varying and finite frequency fields. While there are existing results in the literature for the zero frequency response that appear to be in disagreement with each other, we show that the apparent differences between them vanish with the use of various sum rules, and that our result is in agreement with them. Although our strategy is based on the use of Wannier functions, we show that our result can be written in a ``gauge invariant" form involving Bloch functions. We can write it as the sum of terms that involve the diagonal elements of the Berry connection, and this decomposition is particularly useful in considering the limit of isolated molecules. But these contributions can be repackaged to give a form independent of those diagonal elements, which is thus generally more suitable for numerical computation. We consider an h-BN model to demonstrate the practical considerations in building a model and making calculations within this formalism.

cond-mat.mes-hall↗

arXiv2023

Magnetoelectric polarizability and optical activity: spin and frequency dependence

We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons, introducing a general spin orbit coupling and Zeeman interaction term in the Hamiltonian. At finite frequencies and including spin, the magnetoelectric polarizability tensor is replaced by two separate tensors, one that relates the polarization \textbf{P} to the magnetic field \textbf{B} and a separate tensor that relates the magnetization \textbf{M} to the electric field \textbf{E}. When combined with other relevant response tensors a third rank tensor that relates the induced current density to gradients in the electric field can be introduced; it is gauge invariant, in a form suitable for numerical calculations, and describes optical activity -- including spin effects -- even in materials that may lack time reversal symmetry.

cond-mat.mes-hall↗

arXiv2023

Integrated photonic sources of frequency-bin-encoded multipartite entangled states

We demonstrate that genuine multipartite entangled states can be generated using frequency bin encoding in integrated photonic platforms. We introduce a source of four-photon GHZ states, and a source of three-photon W states. We predict generation rates on the order of 10$^4$ Hz for a silicon microring source with milliwatt pump powers. These results, along with the versatility and scalability of integrated structures, identify this as a promising approach for the generation of higher-dimensional and larger entangled states.

quant-ph↗

arXiv2023

Polarization and orbital magnetization in Chern insulators: A microscopic perspective

We derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator in its zero-temperature ground state using a previously developed formalism for treating microscopic polarization and magnetization fields in extended media. In the limit of a topologically trivial insulator, our results reduce to those of the "modern theories of polarization and magnetization." In a Chern insulator, however, we find a generically nonvanishing microscopic free current density, the macroscopic average of which vanishes. Moreover, the expression that we obtain for the polarization is qualitatively similar to that of the "modern theory," while the expressions for the orbital magnetization fundamentally differ; the manner in which they differ elucidates the distinct philosophies of these theoretical frameworks.

cond-mat.mes-hall↗

arXiv2023

Electric polarization and magnetization in metals

A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect to which general definitions of microscopic electronic polarization and magnetization fields, and free charge and current densities are always admitted. These definitions assume no particular initial electronic state of the crystal, and the set of microscopic fields satisfy the usual relations of classical electrodynamics. Notably, when applied to a trivial insulator initially occupying its $T=0$ ground state, the expressions for the unperturbed polarization and orbital magnetization, and for the orbital magnetoelectric polarizability tensor obtained from these different approaches can agree. However, the "modern theory of magnetization" has been extended via thermodynamic arguments to include metals and Chern insulators. We here compare with that generalization and find disagreement; the manner in which the expressions differ elucidates the distinct philosophies of these approaches. Our approach leads to the usual electrical conductivity tensor in the long-wavelength limit; in the absence of any scattering mechanisms, the dc divergence of that tensor is due to the free current density and the finite-frequency generalization of the anomalous Hall contribution arises from a combination of bound and free current densities. As well, in the limit that the electronic ground state is that of a trivial insulator, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

cond-mat.mes-hall↗

arXiv2023

Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization

We formulate a non-relativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and magnetization field operators whose moments are identified with the multipole moments of the charge-current distribution. The multipolar Hamiltonian is obtained from the minimal coupling Hamiltonian through a unitary transformation, often referred to as the Power-Zienau-Woolley transformation; we renormalize this Hamiltonian using perturbation theory, the result of which is used to compute the leading-order radiative corrections to the electronic energy levels due to interactions between the electrons and quantum vacuum fluctuations in the electromagnetic field. Our renormalized energy shift constitutes a generalization of the Lamb shift in atomic hydrogen, valid for general localized assemblies of atoms and molecules, possibly with net charge but absent free current. By expanding the fields in a series of multipole moments, our results can be used to study contributions to this energy shift coming from specific multipole moments of arbitrary order.

physics.atom-ph↗

arXiv2023

A reconfigurable silicon photonics chip for the generation of frequency bin entangled qudits

Quantum optical microcombs in integrated ring resonators generate entangled photon pairs over many spectral modes, and allow the preparation of high dimensional qudit states. Ideally, those sources should be programmable and have a high generation rate, with comb lines tightly spaced for the implementation of efficient qudit gates based on electro-optic frequency mixing. While these requirements cannot all be satisfied by a single resonator device, for which there is a trade-off between high generation rate and tight bin spacing, a promising strategy is the use of multiple resonators, each generating photon pairs in specific frequency bins via spontaneous four-wave mixing. Based on this approach we present a programmable silicon photonics device for the generation of frequency bin entangled qudits, in which bin spacing, qudit dimension, and bipartite quantum state can be reconfigured on-chip. Using resonators with a radius of 22 microns, we achieve a high brightness (MHz/(mW)^2) per comb line with a bin spacing of 15 GHz, and fidelities above 85% with maximally entangled Bell states up to a Hilbert space dimension of sixteen. By individually addressing each spectral mode, we realize states that can not be generated on-chip using a single resonator. We measure the correlation matrices of maximally entangled two-qubit and two-qutrit states on a set of mutually unbiased bases, finding fidelities exceeding 98%, and indicating that the source can find application in high-dimensional secure communication protocols.

quant-ph↗

arXiv2023

Generation of photon pairs by spontaneous four-wave mixing in linearly uncoupled resonators

We present a detailed study of the generation of photon pairs by spontaneous four-wave mixing in a structure composed of two linearly uncoupled resonators, where energy can be transferred from one resonator to another only through a nonlinear interaction. Specifically, we consider the case of two racetrack-shaped resonators connected by a coupler designed to guarantee that the resonance comb of each resonator can be tuned independently, and to allow the nonlinear interaction between modes that belong to different combs. We show that such a coupler can be realized in at least two ways: a directional coupler or a Mach-Zehnder interferometer. For these two scenarios, we derive analytic expressions for the pair generation rate via single-pump spontaneous four-wave mixing, and compare these results with that achievable in a single ring resonator.

quant-ph↗

arXiv2022

Two strategies for modeling nonlinear optics in lossy integrated photonic structures

We present two complementary strategies for modeling nonlinear quantum optics in realistic integrated optical devices, where scattering loss is present. In the first strategy, we model scattering loss as an attenuation; in the second, we employ a Hamiltonian treatment that includes a mechanism for scattering loss, such as a `phantom waveguide.' These strategies can be applied to a broad range of structures and processes. As an example, we use these two approaches to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an add-drop system. Even for these well-understood systems, our strategies yield some novel results. We show the rates of photon pairs, broken pairs, and lost pairs and their dependence on system parameters. We show that the properties of lost and broken photon pairs in such structures can be related to those of the un-scattered photon pairs, which are relatively simple to measure.

quant-ph↗

arXiv2022

Theory of Optical Activity in Doped Systems with Application to Twisted Bilayer Graphene

We theoretically study the optical activity in a doped system and derive the optical activity tensor from a light wavevector-dependent linear optical conductivity. Although the light-matter interaction is introduced through the velocity gauge from a minimal coupling Hamiltonian, we find that the well-known ``false divergences'' problem can be avoided in practice if the electronic states are described by a finite band effective Hamiltonian, such as a few-band tight-binding model. The expression we obtain for the optical activity tensor is in good numerical agreement with a recent theory derived for an undoped topologically trivial gapped system. We apply our theory to the optical activity of a gated twisted bilayer graphene, with a detailed discussion of the dependence of the results on twist angle, chemical potential, gate voltage, and location of rotation center forming the twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2022

Super spontaneous four-wave mixing in an array of silicon microresonators

Composite optical systems can show compelling collective dynamics. For instance, the cooperative decay of quantum emitters into a common radiation mode can lead to superradiance, where the emission rate of the ensemble is larger than the sum of the rates of the individual emitters. Here, we report experimental evidence of super spontaneous four-wave mixing (super SFWM), an analogous effect for the generation of photon pairs in a parametric nonlinear process on an integrated photonic device. We study this phenomenon in an array of microring resonators on a silicon photonic chip coupled to bus waveguides. We measured a cooperative pair generation rate that always exceeds the incoherent sum of the rates of the individual resonators. We investigate the physical mechanisms underlying this collective behaviour, clarify the impact of loss, and address the aspects of fundamental and technological relevance of our results.

quant-ph↗

arXiv2022

Resonant and non-resonant integrated third order parametric down-conversion

Third order parametric down-conversion describes a class of nonlinear processes in which a pump photon can be down-converted into triplets of photons. It has been identified as a source of non-classical light, with capabilities beyond those offered by better-established processes such as spontaneous four-wave mixing. Here we discuss the implementation of TOPDC in integrated photonic systems. We derive equations for the rates of TOPDC in a non-resonant (waveguide) and resonant (microring) platform, such that the scaling with experimental parameters can be plainly seen. We find that generally non-resonant platforms should be pursued for spontaneous TOPDC (SpTOPDC), whereas resonant platforms are more suitable for stimulated TOPDC (StTOPDC). We present a sample calculation for TOPDC rates in sample systems with conservative and accessible parameters. We find that StTOPDC should be observable with the current fabrication technology, and that with some progress in the design of TOPDC platforms, integrated SpTOPDC too could be demonstrated in the near term.

quant-ph↗

arXiv2022

Generation of Photon Pairs by Stimulated Emission in Ring Resonators

Third-order parametric down-conversion (TOPDC) describes a class of nonlinear interactions in which a pump photon is converted into a photon triplet. This process can occur spontaneously, or it can be stimulated by seeding fields. In the former case, one typically has the generation of non-Gaussian states of light. In the latter, the situation is more variegated, for stimulated TOPDC (StTOPDC) can be implemented in many ways, depending on the number and properties of the seeding fields. Here we show that StTOPDC can be exploited for the generation of quantum correlated photon pairs. We examine the peculiar features of this approach when compared with second-order spontaneous parametric down-conversion and spontaneous four-wave mixing. We model StTOPDC in a microring resonator, predicting observable generation rates in a microring engineered for third-harmonic generation. We conclude that if the experimental difficulties associated with implementing StTOPDC can be overcome, it may soon be possible to demonstrate this process in resonant integrated devices.

quant-ph↗

arXiv2021

From magnetoelectric response to optical activity

We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into "site" polarization and magnetization fields, from which "site multipole moments" can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them; for electromagnetic fields varying little over a lattice constant these are the electric and magnetic dipole moments per unit volume, and the electric quadrupole moment per unit volume. A description of optical activity and related magneto-optical phenomena follows from the response of these macroscopic quantities to the electromagnetic field and, while in this paper we work within the independent particle and frozen-ion approximations, both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.

cond-mat.mes-hall↗

arXiv2021

Beyond photon pairs: Nonlinear quantum photonics in the high-gain regime

Integrated optical devices will play a central role in the future development of nonlinear quantum photonics. Here we focus on the generation of high-gain nonclassical light within them. Starting from the solid foundation provided by Maxwell's equations, we then move to applications by presenting a unified formulation that allows for a comparison of stimulated and spontaneous experiments in ring resonators and nanophotonic waveguides, and leads directly to the calculation of the quantum states of light generated in high-gain experiments.

quant-ph↗