Comparison of Spatial Entanglement between dissociated atom and ion : molecular ion photo-dissociated by sequential two-photon absorption and correlated two-photon absorption
Krishna Rai Dastidar
quant-phSubmitted Jul 31, 2026• Announced Aug 3, 2026• 0 citations• Revised Aug 3, 2026 (v2)
We have studied the fidelity of spatial entanglement between dissociated atom and ion from two photon dissociation of hydrogen molecular ion H 2 + . Two processes for two photon dissociation of molecular ion have been considered (i) sequential two photon (STP) absorption and (ii) correlated two photon (CTP) absorption by the molecular ion. We compared the results for fidelity of spatial entanglement (FSE) between dissociated atom and ion for these two types of dissociation. In a previous study in our group [1] we have shown that when an atom interact with nonlocal mode of electromagnetic field (which has been derived field theoretically), simultaneous phase-correlated two pho1 ton absorption by the atom occurs within a very short time δt << ω , where ω is the laser frequency, and the rate of this correlated two photon absorption is linear in intensity. This will happen when the photon flux in the interaction region is high i.e. laser intensity is higher than 10 10 W/cm 2 . In this work we have extended this formalism to study the correlated two photon dissociation of molecular ion and to explore the effect of correlation between two simultaneous photo-absorption processes on the fidelity for spatial entanglement of dissociated atom and ion. Dependence of fidelity for spatial entanglement on the photon frequency has been studied for both the STP and CTP dissociation, to show that photon frequency can be used as control parameter to achieve maximum fidelity. Saturation of fidelity with the increase in time at which fidelity was calculated shows the robustness of the processes considered here. A scheme for detection of spatial entanglement between ion and atom has been suggested.
We have studied the fidelity of spatial entanglement between dissociated atom and ion from two photon dissociation of hydrogen molecular ion H 2 + . Two processes for two photon dissociation of molecular ion have been considered (i) sequential two photon (STP) absorption and (ii) correlated two photon (CTP) absorption by the molecular ion. We compared the results for fidelity of spatial entanglement (FSE) between dissociated atom and ion for these two types of dissociation. In a previous study in our group [1] we have shown that when an atom interact with nonlocal mode of electromagnetic field (which has been derived field theoretically), simultaneous phase-correlated two pho1 ton absorption by the atom occurs within a very short time δt << ω , where ω is the laser frequency, and the rate of this correlated two photon absorption is linear in intensity. This will happen when the photon flux in the interaction region is high i.e. laser intensity is higher than 10 10 W/cm 2 . In this work we have extended this formalism to study the correlated two photon dissociation of molecular ion and to explore the effect of correlation between two simultaneous photo-absorption processes on the fidelity for spatial entanglement of dissociated atom and ion. Dependence of fidelity for spatial entanglement on the photon frequency has been studied for both the STP and CTP dissociation, to show that photon frequency can be used as control parameter to achieve maximum fidelity. Saturation of fidelity with the increase in time at which fidelity was calculated shows the robustness of the processes considered here. A scheme for detection of spatial entanglement between ion and atom has been suggested.
This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.
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.
The Two-photon absorption processes (TPA) is of great interest due to its variety of technical applications. Two-photon transitions can be excited using light with different statistical properties, such as laser light (coherent light), pseudo-thermal light and entangled photons-pairs (ETPA). For a TPA process driven with entangled photons (ETPA), a linear dependence of the signal with the photon flux has been theoretically predicted and experimentally demonstrated by various groups. The main motivation for studying ETPA relies on the capability of inducing TPA with a low photon flux. This is advantageous to analyze, among other things, biological samples with a reduced probability of destroying them in the process. However, ETPA experiments developed to date raise many questions regarding the difficulty of isolating a signal in organic molecules. One of the main problems in these experiments is the difficulty to study independently all the systematic effects due to the complex structure of organic molecules. An alternative to clarify the origin of the signal is to study the ETPA process in atomic systems. In this case, the possibility to excite narrow band transitions with tunable single frequency lasers can provide a clear signature of the ETPA process. To achieve this objective, the first step consists of understanding TPA with coherent light, or classical TPA, and measuring the corresponding cross-section in atomic systems. Once the classical regime is characterized, the ETPA process can be studied considering decoherence effects and coherence between intermediate states. For this, the ETPA cross section must be calculated and measured. In this work we present a theoretical calculation of the ETPA transition probability and cross-section with the density operator formalism for the transition 62S1/2 →82S1/2. The theoretical results will be complemented with an experiment with atomic Cesium based in a coincidence detection scheme.
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents 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 and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given.
The interaction of single photons with single atoms is a fundamental process in quantum optics which manifests the quantum mechanical nature of light and matter. As an experimentally controlled process it enables the implementation of quantum technological applications, such as quantum information processing and quantum metrology. In the last decades, substantial progress has been attained to experimentally control and manipulate single atoms.
For example, single or multiple ions can be stored in an ion trap and their quantum states can be controlled with great precision. At the same time, experimental techniques to generate and control single photons and entangled photon pairs have been widely developed. However, only modest progress has been attained in controlling the interaction of single atoms with sin~le photons. The aim of this thesis project was to experimentally study he absorption of single photons and entangled photons pairs by single trapped DCa· ions. To this end, a source of polarization-entangled photon pairs based on the process of spontaneous parametric down-conversion (SPDC) was designed and constructed . Generating photon pairs whose interaction with an atom can be controlled imposed stringent requirements on the bandwidth, tunability, stability and brightness of the source, making its setup much more complex than usual SPDC sources. In a parallel project, a set of two separate ion traps were built, capable of storing a single or a set of a few 4DCa· ions.
he first part of the thesis documents the design, construction , operation and characterization of the entangled photon pair source. The characterization proves all the necessary requirements for the photons to interact with either of two transitions, D312 P312 and D5i2 P312 at 850 and 854 nm respectively, in 4DCa· One of the crucial requirements was to make the source bandwidth match the bandwidth of these transitions (22MHz). This was not straightforward since the typical emission bandwidths of the SPDC process is several orders of magnitude higher (1 05MHz). The ion trap setup is also briefly described. One of its crucial features is the inclusion of two high numerical-aperture objectives very close to the ion trap, allowing to enhance the interaction efficiency of the SPDC photons with the ion, and to efficiently collect the fluorescence light they emit. In a second part of the thesis, a concise description of the schemes and techniques used to detect the absorption of single photons by a single trapped ion is given, including a heoretical treatment of the methods used to analyze the data.
he core part of the thesis describes the methods used to couple the entangled photon source to one of the ion traps, and explains the results obtained with the combined setup. First it shows how the source is configured to produce heralded single photons. It then presents experiments in which the absorption by a single ion of photons produced by the source is detected, and how these absorption events are time-correlated with the detection of the heralding photon. These experiments are performed under several conditions, with a growing level of control over the interaction process. Finally, two proof-of-principle experiments are presented. In the first one, the ion is pumped to polarization-sensitive Zeeman substates and the polarization dependence of the correlated absorption rate is observed. This is a first step toward more advanced experiments in which the polarization entanglemen of the photon pairs is transferred to the entanglement of one photon with one atom or to two distant atoms. A second experiment performs heralded single photon spectroscopy on a single ion, showing the expected frequency dependence of the absorption process.
Finally, methods to extend these experiments to implement entanglement transfer from photons to atoms are outlined. In particular, it is shown how the efficiency of the source can be improved to make these experiments feasible.
High-fidelity entanglement of neutral cold atoms can be achieved by combining several already available techniques such as the creation or dissociation of neutral diatomic molecules, manipulating atoms with microfabricated structures (atom chips), and detecting single atoms with almost 100% efficiency. The fidelity of the resulting entanglement is robust against the details of dissociation process. Manipulating this entanglement with integrated or linear atom optics will open a perspective for quantum-information processing with neutral atoms.