Two-photon Wave Packet Research Articles

Exact solution of a lambda quantum system driven by a two-photon wave packet

Three-level atoms in lambda configuration find diverse applications in quantum information processing, and a promising way to manipulate their quantum states is with single-photon pulses propagating in a waveguide (which can be theoretically regarded as a highly broadband regime of the Jaynes–Cummings model). Here, we analytically find the nonperturbative dynamics of a lambda atom driven by a two-photon wave packet, propagating in a 1D electromagnetic environment. We study the dynamics of a quantum state purification as an application. By comparing our exact model with an approximated model of two cascaded single-photon wave packets, we show how two-photon nonlinearities and stimulated emission affect the purification.

Input–output wavepacket description of two photons interacting with a V-type three-level atom in an optical cavity

We study the interaction of a V-type atom in a cavity with incident single- and two-photon wavepackets and derive an exact formula, valid in all parameter regimes, relating the spectrum of the outgoing wavepackets to the incident one. We present detailed results for several special input pulses and consider the potential performance of the system as a CPHASE gate for initial pulses in a product state. We find values of the cavity, atomic, and pulse parameters that yield a conditional phase shift of π, albeit with a relatively small overlap between the incoming and outgoing pulse forms.

Spectrally resolved two-photon interference in a modified Hong–Ou–Mandel interferometer

A modified Hong–Ou–Mandel (HOM) interference reveals that the two-photon interference phenomenon can be explained only by the concept of a two-photon wave packet rather than a single-photon one. However, the temporal interferogram in the modified HOM interferometer becomes flat in some cases so that no useful information can be extracted from time-domain measurement. Here, we theoretically explore such temporal interferogram from the frequency domain and obtain the spectrally resolved interference with high visibility. The result represents a modulation of the joint spectral intensity along both the frequency sum and the frequency difference directions. This is quite different from the cases of the spectrally resolved HOM interference and N00N state interference where the modulations happened only in one direction. Moreover, we have shown that such modulations have a potential application in the generation and characterization of high-dimensional frequency entanglement.

Dynamical photon–photon interaction mediated by a quantum emitter

Single photons constitute a main platform in quantum science and technology: they carry quantum information over extended distances in the future quantum internet and can be manipulated in advanced photonic circuits enabling scalable photonic quantum computing. The main challenge in quantum photonics is how to generate advanced entangled resource states and efficient light-matter interfaces. Here we utilize the efficient and coherent coupling of a single quantum emitter to a nanophotonic waveguide for realizing quantum nonlinear interaction between single-photon wavepackets. This inherently multimode quantum system constitutes a new research frontier in quantum optics. We demonstrate control of a photon with another photon and experimentally unravel the dynamical response of two-photon interactions mediated by a quantum emitter, and show that the induced quantum correlations are controlled by the pulse duration. The work will open new avenues for tailoring complex photonic quantum resource states.

Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in the dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes, forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here, we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to an analytical treatment for a number of timely problems such as the system interaction with two-photon wave packets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules.

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Optimal two-photon excitation of bound states in non-Markovian waveguide QED

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single-photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this Letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave packets that can excite a given superposition of these bound states. As specific examples, we study bound-state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

Deterministic generation of high-dimensional entanglement between distant atomic memories via multiphoton exchange

Promising access to high-speed quantum networks relies on the creation of high-dimensional entangled memories that provide quantum communication with higher capacity of noisy quantum channels, thereby reducing the transmission time of information. Yet, the distribution of multidimensional entanglement between remote memory nodes is still faintly investigated. We propose an experimentally feasible protocol of deterministic generation of high-dimensional entanglement between distant multilevel atoms confined in high-finesse optical cavities and driven by laser pulses. Three-dimensional entanglement is generated deterministically between remote atoms by triggering a two-photon wave packet, which mediates a superposition of states chosen by the laser pulse parameters. The efficient transfer of atomic states between remote nodes allows the construction of a three-dimensional quantum repeater, where the successful creation of entanglement can be verified by a simple method for reliable measurement of atomic ground Zeeman states.

Energy-time-entangled two-photon molecular absorption

Nonlinear spectroscopy and microscopy techniques are ubiquitous in a wide range of applications across physics and biology. However, these usually rely on high-powered pulsed laser systems. A promising alternative is to exploit entangled two-photon absorption (ETPA), which can lead to tens of orders of magnitude lower incident flux rates than in conventional two-photon absorption (TPA) schemes. However, the role of different entangled degrees of freedom in ETPA was unclear following recent experimental studies, when compared to earlier theoretical works. Here, we first demonstrate a linear dependence of the ETPA rate with the photon-pair flux, a clear signature of ETPA, and estimate the first values for the concentration-dependent ETPA cross-section for Rhodamine 6G.We then investigate the signature of energy-time entanglement and polarization dependence in the ETPA fluorescence rate and demonstrate a strong dependence of the signal on the inter-photon delay that reflects the coherence time of the entangled two-photon wave-packet.

Disorder-protected quantum state transmission through helical coupled-resonator waveguides

We predict the preservation of temporal indistinguishability of photons propagating through helical coupled-resonator optical waveguides (H-CROWs). H-CROWs exhibit a pseudospin-momentum locked dispersion, which we show suppresses on-site disorder-induced backscattering and group velocity fluctuations. We simulate numerically the propagation of two-photon wave packets, demonstrating that they exhibit almost perfect Hong–Ou–Mandel dip visibility and then can preserve their quantum coherence even in the presence of moderate disorder, in contrast with regular CROWs, which are highly sensitive to disorder. As indistinguishability is the most fundamental resource of quantum information processing, H-CROWs may find applications for the implementation of robust optical links and delay lines in the emerging quantum photonic communication and computational platforms.

Few-photon Fock-state wave packet interacting with a cavity-atom system in a waveguide: Exact quantum state dynamics

In the paper, we employ a wavefunction approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave packet scattered from the JC system experience transformation for nonzero atom-cavity couplings. Moreover, using Schmidt decomposition, we show that the scattered photons feature frequency entanglement contrary to the incident ones which are not entangled.

Dispersive Broadening of Two-photon Wave Packets Generated via Type-I and Type-II Spontaneous Parametric Down-conversion

Photons generated via spontaneous parametric down-conversion (SPDC) have broad spectrums and suffer from dispersive broadening of the temporal wave packets when they are transmitted through dispersive media. In this paper we theoretically and experimentally study the detailed amount of the temporal broadening of the two-photon wave packets generated via both type-I and type-II SPDC with β-BaB2O4 of various lengths, by transmitting them through optical fibers. We interpret the results with respect to the spectral properties of the two-photon wave packets. We believe that our results will contribute to implementing protocols involving long-range distributions of photon pairs.

Reversible storage of entangled two-mode wavepacket based on electromagnetically induced transparency

We discuss the reversible storage of an entangled two-mode wavepacket in separated two atomic ensembles based on electromagnetically induced transparency. By introducing wavepacket dark-states, we show the dynamic transfer of quantum information of the wavepacket between the optical field and the atomic ensembles. We examine in detail the performance of the scheme focusing on the reversible storage of an entangled two-photon wavepacket in the case where the effects of the environment and the thermal motions of atoms are taken into consideration.

Relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherently-pumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transverse-momentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.

Two-photon interference of temporally separated photons.

We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.

Highly indistinguishable on-demand resonance fluorescence photons from a deterministic quantum dot micropillar device with 74% extraction efficiency.

The implementation and engineering of bright and coherent solid state quantum light sources is key for the realization of both on chip and remote quantum networks. Despite tremendous efforts for more than 15 years, the combination of these two key prerequisites in a single, potentially scalable device is a major challenge. Here, we report on the observation of bright single photon emission generated via pulsed, resonance fluorescence conditions from a single quantum dot (QD) deterministically centered in a micropillar cavity device via cryogenic optical lithography. The brightness of the QD fluorescence is greatly enhanced on resonance with the fundamental mode of the pillar, leading to an overall device efficiency of η = (74 ± 4) % for a single photon emission as pure as g(2)(0) = 0.0092 ± 0.0004. The combination of large Purcell enhancement and resonant pumping conditions allows us to observe a two-photon wave packet overlap up to ν = (88 ± 3) %.

Generation, manipulation, and detection of two-qubit entanglement in waveguide QED

We study the possibility of using guided photons to generate, control, and measure the entanglement of two qubits that is mediated by a one-dimensional waveguide. We show how entanglement can be generated both with single photon and with two-photon wavepackets. The introduction of a second photon allows for a manipulation of the entanglement between the qubits, and phenomena such as sudden death and revival of entanglement appear. Finally, we propose a procedure for entanglement detection via the scattering output of a single-photon over a qubit state.

Probability amplitudes for broadband N-photon processes in linear optics

Advances in the production of multiple-photon states with a broadband spectrum and its subsequent processing through linear optical systems demand simple rules to automate the calculation of probability amplitudes. A methodology to write down directly the probability amplitude of any broadband multi-photon process in linear optics is proved. A physically intuitive notion of multi-photon paths is derived from Wick’s theorem and amplitudes are formulated as sums over paths. Every permutation of the out-state photon frequencies over the photon occupation indices that the in-state wavepacket assigns to the inports contributes a path. A simple general rule is provided to compute them. Broadband two-photon processes in the interferometers by Hong, Ou and Mandel (HOM) and by Mach and Zehnder (MZ) are considered. We provide a rigorous description of the HOM interferometer as a probe of the amount of frequency entanglement contained in some two-photon wavepackets, establishing an integral transform between the interference profile and the spectral density of frequency-entangled photon pairs. For the MZ interferometer, our method provides the exact rate of coincidence counts for a broadband two-photon process that is relevant for pairs produced with a wide two-dimensional spectral bandwidth by spontaneous parametric downconversion.

Transverse compression of two-photon wave packets

A method for generating two-photon wave packets (biphotons) with a small width of the spatial intensity correlation function (correlation radius) has been considered. We propose to prepare a two-photon wave packet inhomogeneously broadened in the angle by means of spontaneous parametric down-conversion in an inhomogeneous crystal. Such biphotons are not diffraction limited; i.e., their correlation radius is much larger than the inverse width of the spatial spectrum. However, the correlation radius of such a biphoton decreases as the biphoton propagates in free space, and transverse compression occurs at a certain distance from the crystal; i.e., the biphoton becomes diffraction limited.

Biphoton compression in a standard optical fiber: Exact numerical calculation

The generation of two-photon wave packets, produced by spontaneous parametric down-conversion in crystals with linearly chirped quasi-phase-matching grating, is analyzed. Although they are spectrally broad, two-photon wave packets produced in this way are not Fourier-transform limited. We discuss the temporal compression of the wave packets, exploiting the insertion of a standard optical fiber in the path of one of the two photons. The effect is analyzed by means of full numerical calculation, and the exact dispersion dependencies in both the crystal and the fiber are considered. The study paves the way for practical realization of this idea.