While two-photon absorption (TPA) and other forms of nonlinear interactions of molecules with isolated time-frequency-entangled photon pairs (EPP) have been predicted to display a variety of fascinating effects, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents a detailed theoretical study of quantum-enhanced TPA by both photon-number correlations and spectral correlations, including an account of the deleterious effects of dispersion. While such correlations in EPP created by spontaneous parametric down conversion can increase the TPA rate significantly in the regime of extremely low optical flux, we find that for typical molecules in solution this regime corresponds to such low TPA event rates as to be unobservable in practice. Our results support the usefulness of EPP spectroscopy in atomic or other narrow-linewidth systems, while questioning the efficacy of such approaches for broadband systems including molecules in solution.
We experimentally study entangled two-photon absorption in Rhodamine 6G as a function of the spatial properties of a high flux of broadband entangled photon pairs. We first demonstrate a key signature dependence of the entangled two-photon absorption rate on the type of entangled pair flux attenuation: linear, when the laser pump power is attenuated, and quadratic, when the pair flux itself experiences linear loss. We then perform a fluorescence-based Z-scan measurement to study the influence of beam waist size on the entangled two-photon absorption process and compare this to classical single…
By going beyond Hubbard Hamiltonian we reflected correlation effects accurately in the wavefunctions of H2. Using ab initio e-e interaction parameters resulted maximally entangled ground and third excited states. We assigned this maximally entangled character to the nonmagnetic (S=0) property of these states and also the minimally entangled character of the first excited states to its magnetic property. By switching on a magnetic field an entangled state with Sz = 0 can be extracted from a minimally entangled degenerate magnetic state. We suggest that presence of a moderate correlated system a…
he multiqubit entangled states are coherently controlled in the quantum spin systems composed of $N+1$ interacting antiferromagnetic molecular rings. The tunable intermolecular couplings arise from the local exchange interactions between electron spins of $N$ circumjacent magnets and those of one central molecular ring. The quantum dynamics of such system is analytically deduced by the effective spin hamiltonian with anisotropic Heisenberg couplings. It is found that entangled $W$ states can be generated with a high precision under the circumstance of quantum fluctuations. The multiqubit entan…
We calculate the rate of two-photon absorption for frequency entangled photons in a tapered optical fiber whose diameter is comparable to the wavelength of the light. The confinement of the electric field in the transverse direction increases the intensity associated with a single photon, while the two-photon absorption rate is further enhanced by the fact that the sum of the frequencies of the two photons is on resonance with the upper atomic state, even though each photon has a relatively broad linewidth. As a result, the photons are effectively confined in all three dimensions and the two-p…
Successful generation of photonic cluster states is the key step in the realization of measurement-based quantum computation and quantum network protocols. Several proposals for the generation of such entangled states from different solid-state emitters have been put forward. Each of these protocols come with their own challenges in terms of both conception and implementation. In this work we propose deterministic generation of these photonic cluster states from a spin-photon interface based on a hole spin qubit hosted in a quantum dot molecule. Our protocol resolves many of the difficulties o…
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 dep…
Excitation with entangled photon pairs may lead to an increase in the efficiency of two-photon absorption at low photon flux. The corresponding process, entangled two-photon absorption (E2PA), has been investigated in numerous theoretical and experimental studies. However, significant ambiguity and inconsistency remain in the literature about the absolute values of E2PA cross-sections. Here, we use a fluorescence-based registration scheme to experimentally determine upper bounds on the cross-sections for six fluorophores. These bounds are up to four orders of magnitude lower than the smallest …
We investigate how entanglement can enhance two-photon absorption in a three-level system. First, we employ the Schmidt decomposition to determine the entanglement properties of the optimal two-photon state to drive such a transition, and the maximum enhancement which can be achieved in comparison to the optimal classical pulse. We then adapt the optimization problem to realistic experimental constraints, where photon pairs from a down-conversion source are manipulated by local operations such as spatial light modulators. We derive optimal pulse shaping functions to enhance the absorption effi…
Light incident upon molecules trigger fundamental processes in diverse systems present in nature. However, under natural conditions, such as sunlight illumination, it is impossible to assign known times for photon arrival owing to continuous pumping, and therefore, the photo-induced processes cannot be easily investigated. In this work, we theoretically demonstrate that characteristics of sunlight photons such as photon number statistics and spectral distribution can be emulated through quantum entangled photon pair generated with the parametric down-conversion (PDC). We show that the average …
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs (EPP) has been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents in tutorial style a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory, then we review the density-matrix (Liouville) derivation of molecular optical response, …
We investigate the entanglement properties of multiparticle systems, concentrating on the case where the entanglement is robust against disposal of particles. Two qubits -belonging to a multipartite system- are entangled in this sense iff their reduced density matrix is entangled. We introduce a family of multiqubit states, for which one can choose for any pair of qubits independently whether they should be entangled or not as well as the relative strength of the entanglement, thus providing the possibility to construct all kinds of ''Entanglement molecules''. For some particular configuration…
It has been proposed that entangled two-photon absorption (E2PA) can be observed with up to 10 orders of magnitude lower photon flux than its classical counterpart. However, there is a significant controversy regarding the magnitude of this quantum enhancement in excitation efficiency. We investigated the fluorescence signals from Rhodamine 6G and LDS798 excited with a CW laser or an entangled photon pair source at 1060 nm. We observed a signal that originates from hot-band absorption (HBA), which is one-photon absorption from thermally-populated vibrational levels of the ground electronic sta…
We examine the question of coherent perfect absorption (CPA) of single photons, and more generally, of the quantum fields by a {\it macroscopic} medium. We show the CPA of path entangled single photons in a Fabry-Perot interferometer containing an absorptive medium. The frequency of perfect absorption can be controlled by changing the interferometer parameters like the reflectivity and the complex dielectric constant of the material. We exhibit similar results for path entangled photons in micro-ring resonators. For entangled fields like the ones produced by a down converter the CPA aspect is …
We describe two-photon absorption processes excited by entangled pairs, but not by non-entangled pairs of the same energy and polarization. Photon states are selected for destructive interference in the non-entangled process between different sequences of absorption via multiple intermediate states. A non-zero entangled absorption cross section is obtained by varying the entanglement time and pair delay parameters. Detailed energy and polarization requirements are derived for Rb 5S1/2 --> 5D3/2 transitions. Applications to Quantum Steganography and Quantum Key Distribution are discussed.
We study how photon absorption losses degrade the bipartite entanglement of entangled states of light. We consider two questions: (i) what state contains the smallest average number of photons given a fixed amount of entanglement? and (ii) what state is the most robust against photon absorption? We explain why the two-mode squeezed state is the answer to the first question but not quite to the second question.
Rabi frequencies for multiphoton absorption by atoms or molecules that can be characterized as two- or three-level systems are obtained in the cases of single and double laser perturbations. If the ambiguity in the origin of absolute energy is conveniently gauged off in the three-level model, there appears an additional non linear frequency which is originated from the separate evolution of a relative-frequency component induced in the whole system by the simultaneous action of the two perturbations.
It is proposed in this paper that without a measurement, the wave function of a system periodically transits to a bound energy eigenfunction or the complementary wave function that is orthogonal to all the bound energy eigenfunctions. Applying this assumption to analyze results of position measurement shows that when the wave function of the entangled incident object and a position detector is a linear combination of the bound energy eigenfunctions of the entangled system prior to collapses, the detection rate essentially equals the probability flux of the incident object entering the detector…
Entangled photon pairs have been promised to deliver a substantial quantum advantage for two-photon absorption spectroscopy. However, recent work has challenged the previously reported magnitude of quantum enhancement in two-photon absorption. Here, we present an experimental comparison of sum-frequency generation and molecular absorption, each driven by isolated photon pairs. We establish an upper bound on the enhancement for entangled-two-photon absorption in Rhodamine-6G, which lies well below previously reported values.
An antiferromagnetically exchange-coupled dimer of single molecule magnets which possesses a large spin tunneling has been investigated. For this system the ground and first excited states are entangled states and the Hamiltonian is effectively similar to that of a two-state system at $2s^{\text{th}}$ order in perturbation theory, thus this system can be mapped to an entangled pseudospin 1/2 particles. We study the effects of interaction and rotation of this system about its staggered easy-axis direction . The corresponding Hamiltonian of a rotated two-state entangled spin system is derived wi…
In virtual-state spectroscopy, information about the energy-level structure of an arbitrary sample is retrieved by Fourier transforming sets of measured two-photon absorption probabilities of entangled photon pairs where the degree of entanglement and the delay time between the photons have been varied. This works well for simple systems but quickly becomes rather difficult when many intermediate states are involved. We propose and discuss an extension of entangled two-photon absorption spectroscopy that solves this problem by means of repeated measurements at different pump wavelengths. Speci…
We numerically analyze the use of intense entangled twin beams for ultra-sensitive spectroscopic measurements in chemical and biological systems. The examined scheme makes use of intense frequency-modulated (chirped) entangled beams to successfully extract information about the intermediate material states that contribute to the two-photon excitation of an absorbing medium. Robustness of the presented method is examined with respect to the applied intervals of the frequency chirp.
A class of centrosymmetric molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons with angular momenta that are maximally entangled. The Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric downconversion of light. As in optical settings, the ability to produce Bell states should enable foundati…
We propose a new method to measure the absolute photon absorption cross section of neutral molecules in a molecular beam. It is independent of our knowledge of the particle beam density, nor does it rely on photo-induced fragmentation or ionization. The method is based on resolving the recoil resulting from photon absorption by means of near-field matter-wave interference, and it thus applies even to very dilute beams with low optical densities. Our discussion includes the possibility of internal state conversion as well as fluorescence. We assess the influence of various experimental uncertai…
Quantum light spectroscopy, providing novel molecular information non-accessible by classical light, necessitates new computational tools when applied for complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce the 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-ti…
The properties of non-product states, both (anti)symmetrized and entangled, have been extensively studied in the literature. In this paper, by extending previous partial results, we introduce a general framework to describe atomic absorption and emission in these states. Our approach shows the existence of some fundamental differences between entanglement and (anti)symmetrization and between absorption and emission. For instance, modifications of the emission properties with respect to that of uncorrelated systems occur for any (anti)symmetrized state but only for some very specific entangled …
We develop an ultrafast frequency-resolved Raman spectroscopy with entangled photons for polyatomic molecules in condensed phases, to probe the electronic and vibrational coherences. Using quantum correlation between the photons, the signal shows the capability of both temporal and spectral resolutions that are not accessible by either classical pulses or the fields without entanglement. We develop a microscopic theory for this Raman spectroscopy, revealing the electronic coherence dynamics which often shows a rapid decay within $\sim$50fs. The heterodyne-detected Raman signal is further devel…
We extend entangled coincidence (ghost) imaging to fluorescent samples. Given the entangled photon correlation, one photon of the pair carries information on where the other photon has been absorbed and has produced fluorescence in a sample. Fluorescent molecules serve as ''detectors breaking'' the entanglement.
We analyze atom-atom interactions in optical lattices due to a laser-induced long-range interatomic force which prevails over the usual London-van der-Waals forces. This force, which can be generated by an intense laser field at a wavelength longer than that of the lattice-generating laser, is shown to bind pairs of cold atoms trapped at different lattice sites, and cause their translational quantum correlations (spatial entanglement).
Quantum information science is driving progress in a vast number of scientific and technological areas that cover molecular spectroscopy and matter-light interactions in general. In these fields, the ability to generate quantum mechanically-entangled photons is opening avenues to explore the interaction of molecules with quantum light. This work considers an alternative way of correlating photons by including energy superpositions. We study how the multichromatic quantum superposition, or color superposition of photon-pair states, influences the optical properties of organic chromophores. This…
Traditionally, spectroscopy is performed by examining the position of absorption lines. However, at frequencies near the transition frequency, additional information can be obtained from the phase shift. In this work we consider the information about the transition frequency obtained from both the absorption and the phase shift, as quantified by the Fisher information in an interferometric measurement. We examine the use of multiple single-photon states, NOON states, and numerically optimized states that are entangled and have multiple photons. We find the optimized states that improve over th…
We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high-Q optical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the `absorption free channel.' A concatenation protocol using the absorption free channel allows for quantum communication with single qubits over distances much larger than the coherence length of the channel.
Coherent perfect absorption (CPA) was introduced as a classical optics phenomenon of a standing-wave absorption by a subwavelength film. In this paper, we develop a theory of CPA of quantized standing waves taking account of a subwavelength thickness of the absorber. This approach allows us to merge all known quantum effects of CPA under a single theory and introduce other regimes of CPA including CPA of NOON states with arbitrary number of entangled photons, orthogonally squeezed vacuum states, continuous variable entangled states, and Schrödinger cat states. Detailed analysis of the quantum …
Recent investigations suggest that the use of non-classical states of light, such as entangled photon pairs, may open new and exciting avenues in experimental two-photon absorption spectroscopy. Despite several experimental studies of entangled two-photon absorption (eTPA), there is still a heated debate on whether eTPA has truly been observed. This interesting debate has arisen, mainly because it has been recently argued that single-photon-loss mechanisms, such as scattering or hot-band absorption may mimic the expected entangled-photon linear absorption behavior. In this work, we focus on tr…
We report the measurement of the entangled two photon absorption cross section, $σ_E$, at 808 nm on organic chromophores in solution in a low photon flux regime. We performed measurements on Zinc tetraphenylporphyrin (ZnTPP) in Toluene and Rhodamine B (RhB) in Methanol. This is, to the best of our knowledge, the first time that $σ_E$ is measured for RhB. Additionally, we report a systematic study of the dependence of $σ_E$ on the molecular concentration for both molecular systems. In contrast to previous experiments, our measurements are based on detecting the pairs of photons that are transmi…
This paper presents properties of the so-called quasi-Bell states: entangled states written as superpositions of nonorthogonal states. It is shown that a special class of those states, namely entangled coherent states, are more robust against decoherence due to photon absorption than the standard bi-photon Bell states.
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Our results provide evidence that this entanglement transfer by dissipation is feasible yielding to a steady-state amount of entanglement in the bipartite quantum syste…
We analyze theoretically the entanglement between two non-planar and light identical molecules (e.g., pyramidal as $NH_3$) that present inversion doubling due to the internal spatial inversion of their nuclear conformations by tunneling. The peculiarity of this system lies in the simplicity of this type of molecular system in which two near levels can be connected by allowed electric dipole transition with considerable value of the dipole moment transition and negligible spontaneous emission because the transition is in the microwave or far-infrared range. These properties give place to entang…
Entangled two-photon absorption spectroscopy (TPA) has been widely recognized as a powerful tool for revealing relevant information about the structure of complex molecular systems. However, to date, the experimental implementation of this technique has remained elusive, mainly because of two major difficulties. First, the need to perform multiple experiments with two-photon states bearing different temporal correlations, which translates in the necessity to have at the experimenter's disposal tens, if not hundreds, of sources of entangled photons. Second, the need to have \emph{a priori} know…
When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We present a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrati…
Entangled Two-Photon Absorption in Cesium Atoms and the Limitations of the Far-Off-Resonance Approximation
Laboratorio de Óptica Cuántica, Universidad de los Andes（安第斯大学量子光学实验室）；Escuela De Ciencias Exactas E Ingeniería, Universidad Sergio Arboleda（塞尔吉奥·阿尔博莱达大学精确科学与工程学院）
In the discussion about the quantumness of NMR computation a conclusion is done that computational states are separable and therefore can not be entangled. This conclusion is based on the assumption that the initial density matrix of an individual molecule coincides with whole sample molecules distribution over single molecule energy levels. This means that quantum stochasticity is replaced by classical stochasticity. In the present paper it is shown, that quantum NMR computation can create genuine entangled states if initial system states are thermodynamical equilibrium ones. A separability a…
Core-excitations on different atoms are highly localized and therefore decoupled. By placing molecules in an X-ray cavity the core-transitions become coupled via the exchange of cavity photons and form delocalized hybrid light-matter excitations known as core-polaritons. We demonstrate these effects for the two inequivalent carbon atoms in 1,1-difluoroethylene. Polariton signatures in the X-ray absorption, two-photon absorption, and multidimensional four-wave mixing, signals are predicted.
We introduce and study the concept of a reversible transfer of the quantum state of two internally-translationally entangled fragments, formed by molecular dissociation, to a photon pair. The transfer is based on intracavity stimulated Raman adiabatic passage and it requires a combination of processes whose principles are well established.
Recently, different experimental methods to investigate the entangled two-photon absorption (ETPA) process in a variety of materials have been reported. The present work reports on a different approach on which the ETPA process is detected based on the changes induced on the Hong-Ou-Mandel (HOM) interferogram of two photons produced by a spontaneous parametric down conversion (SPDC) Type-II process. Using an organic solution of the laser dye Rhodamine B as a model, it is demonstrated that ETPA at 800nm can be monitored by the changes in the temporal-width and visibility of the HOM interferogra…
