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Relative intensity squeezing (RIS) is emerging as a promising technique for performing high-precision measurements beyond the shot-noise limit. A commonly used way to produce RIS in visible/IR range is generating correlated "twin beams" through four-wave mixing by driving atomic resonances with weak laser beams. Here, we propose an all-optical strong-field scheme to produce a series of relative-intensity squeezed high-order harmonic "twin beams". Due to the nature of high harmonics generation the frequencies of the "twin beams" can cover a broad range of photon energy. Our proposal paves the way for the development of nonclassical XUV sources and high precision spectroscopy tools in strong-field regime.

Nonadiabatic dynamics around an avoid crossing or a conical intersection play a crucial role in the photoinduced processes of most polyatomic molecules. The present work shows that the topological phase in conical intersection makes the behavior of pump-probe high-order harmonic spectroscopy different from the case of avoid crossing. The coherence built up when the system crosses the avoid crossing will lead to the oscillatory behavior of the spectrum, while the geometric phase erodes these oscillations in the case of conical intersection. Additionally, the dynamical blueshift and the splitting of time-resolved spectrum allow capturing the snapshot dynamics with sub-femtosecond resolution., Comment: 10 pages, 5 figures

We present a consistent optimization procedure for the optical measurements in open quantum systems using recently developed incoherent control protocol. Assigning an effective hot bath for the two-entangled-photon pump we recast the transmission of classical probe as a work in a quantum heat engine framework. We demonstrate that maximum work in such a heat engine can exceed that for the classical two-photon and one-photon pumps, while efficiency at maximum power can be attributed to conventional boundaries obtained for three-level maser heat engine. Our results pave the way for incoherent control and optimization of optical measurements in open quantum systems that involve two-photon processes with quantum light.

We show that quantum coherence can enhance the performance of a continuous quantum heat engine in the Lindblad description. We investigate the steady-state solutions of the particle-exchanging quantum heat engine, composed of degenerate double quantum dots coupled to two heat baths in parallel, where quantum coherence may be induced due to interference between relaxation channels. We find that the engine power can be enhanced by the coherence in the nonlinear response regime, when the symmetry of coupling configurations between dots and two baths is broken. In the symmetric case, the coherence cannot be maintained in the steady state, except for the maximum interference degenerate case, where initial-condition-dependent multiple steady states appear with a dark state.

We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequence. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways, and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOC) which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOC appear in quantum-informatics studies in other fields, including black holes, high energy, and condensed matter physics., Comment: Supplementary material included

Optical pump-probe signals can be viewed as work done by the matter while transferring the energy between two coherent baths (from pump to probe). In thermodynamics a heat engine, such as laser, is a device which performs similar work but operating between two thermal baths. We propose an "incoherent" control procedure for the optical signals using the physics of quantum heat engine. By combining a coherent laser excitation of electronic excited state of molecule with thermal relaxation we introduce an effective thermal bath treating stimulated emission of probe photons as work performed by the heat engine. We optimize power and efficiency for the pump-probe signal using control parameters of the pump laser utilizing four level molecular model in strong and weak coupling regime illustrating its equivalence with the thermodynamic cycle of the heat engine., Comment: 11 pages, 3 Postscript figures, 1 table

Optical interferometry has been a long-standing setup for characterization of quantum states of light. Both the linear and the nonlinear interferences can provide information about the light statistics an underlying detail of the light-matter interactions. Here we demonstrate how interferometric detection of nonlinear spectroscopic signals may be used to improve the measurement accuracy of matter susceptibilities. Light-matter interactions change the photon statistics of quantum light, which are encoded in the field correlation functions. Application is made to the Hong-Ou-Mandel two-photon interferometer that reveals entanglement-enhanced resolution that can be achieved with existing optical technology.

Relying on the local orientation of nanostructures, Pancharatnam-Berry metasurfaces are currently enabling a new generation of polarization-sensitive optical devices. A systematical mesoscopic description of topological metasurfaces is developed, providing a deeper understanding of the physical mechanisms leading to the polarization-dependent breaking of translational symmetry in contrast with propagation phase effects. These theoretical results, along with interferometric experiments, contribute to the development of a solid theoretical framework for arbitrary polarization-dependent metasurfaces.

We propose a novel quantum diffraction imaging technique whereby one photon of an entangled pair is diffracted off a sample and detected in coincidence with its twin. The image is obtained by scanning the photon that did not interact with matter. We show that when a dynamical quantum system interacts with an external field, the phase information is imprinted in the state of the field in a detectable way. The contribution to the signal from photons that interact with the sample scales as $\propto I_{p}^{1/2}$, where $I_{p}$ is the source intensity, compared to $\propto I_{p}$ of classical diffraction. This makes imaging with weak-field possible, avoiding damage to delicate samples. A Schmidt decomposition of the state of the field can be used for image enhancement by reweighting the Schmidt modes contributions., Comment: In press

Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space $\left|\sigma(\mathbf{q})\right|^{2}$, missing its phase which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals $\sigma(\mathbf{q})$ itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.

Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this letter, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical 3-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a 4-th level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.

Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties - known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators. These are different from Glauber's g- functions for photon counting which use normally ordered products of ordinary operators. Entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.

Coherent multidimensional optical spectroscopy techniques are broadly applied across the electromagnetic spectrum ranging from NMR to the UV. These reveal properties of matter through correlation plots of signal fields generated in response to sequences of short pulses with variable delays. Here we discuss a new class of multidimensional techniques obtained by time-and-frequency resolved photon coincidence counting measurements of N photons which constitutes a 2N dimensional spectrum. A compact description of these signals is developed based on time ordered superoperators rather than the normally ordered ordinary operators used in Glauber's photon counting formalism.The independent control of the time and frequency gate parameters reveals details of matter dynamics not available otherwise. Application to an anharmonic oscillator model with fluctuating energy and anharmonicity demonstrates the power of these signals.

Conical intersections (CoIn) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CoIns have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short X-ray (rather than optical) pulses can directly detect the passage through a CoIn with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond/attosecond X-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CoIn.

Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently-developed ultrashort optical and X-ray pulses via photoexcitation, photoionization and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the phase-sensitive electronic and nuclear dynamics. Three detection protocols of an X-ray broadband probe are compared - frequency dispersed transmission, integrated photon number change, and total pulse energy change. In addition each can be either linear or quadratic in the X-ray probe intensity. These various signals offer different gating windows into the molecular response which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.

Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum spectroscopy signals can be obtained by a simple averaging of their classical spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field; the quantum light thus merely provides a novel gating window for the classical response functions. We show that this argument only applies to the linear response and breaks down in the nonlinear regime. The quantum response carries additional valuable information about response and spontaneous fluctuations of matter that may not be retrieved from the classical response by simple data processing. This is connected to the lack of a nonlinear fluctuation-dissipation relation.

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period $T$, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique known as femtosecond stimulated Raman spectroscopy (FSRS) can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE) originally developed for NMR lineshapes. The SLE provides a convenient simulation protocol that can describe complex dynamics due to coupling to collective coordinates at much lower cost that a full dynamical simulation. The origin of the dispersive features which appear when there is no separation of timescales between vibrational variations and dephasing is clarified.

We predict several effects associated with the optical response of systems prepared in a nonequilibrium state by impulsive optical excitations. The linear response depends on the phase of the electric field even if the initial nonequilirbium state has only populations, no coherences. Initial quantum coherences induce additional phase dependence which also shows new resonances in nonlinear wave mixing. In systems strongly driven by an external optical field, the field frequency generates a phase dependent probe absorption. This gives further control to manipulate the relative contribution to the linear signal due to initial populations and coherences.

We propose a novel femtosecond stimulated Raman spectroscopy (FSRS) technique that combines entangled photons with interference detection to select matter pathways and enhance the resolution. Following photo excitation by an actinic pump, the measurement uses a pair of broadband entangled photons, one (signal) interacts with the molecule together with a third narrowband pulse induces the Raman process. The other (idler) photon provides a reference for the coincidence measurement. This interferometric photon-coincidence counting detection allows to separately measure Raman gain and loss signals, which is not possible with conventional probe transmission detection. Entangled photons further provide a unique temporal and spectral detection window that can better resolve fast excited state dynamics compared to classical and correlated disentangled states of light.

Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle (incoherent) and two-particle (coherent) contributions that carry different particle form factors that involve different material transitions. Single-molecule experiments involving incoherent scattering are more influenced by inelastic processes compared to bulk measurements. The conditions under which the technique directly measures charge densities (and can be considered as diffraction) as opposed to correlation functions of the charge-density are specified. The results are illustrated with time- and wavevector-resolved signals from a single amino acid molecule (cysteine) following an impulsive excitation by a stimulated X-ray Raman process resonant with the sulfur K-edge. Our theory and simulations can guide future experimental studies on the structures of nano-particles and proteins.

Multidimensional optical signals are commonly recorded by varying the delays between time ordered pulses. These control the evolution of the density matrix and are described by ladder diagrams. We propose a new non-time-ordered protocol based on following the time evolution of the wavefunction and described by loop diagrams. The time variables in this protocol allow to observe different types of resonances and reveal information about intraband dephasing not readily available by time ordered techniques. The time variables involved in this protocol become coupled when using entangled light, which provides high selectivity and background free measurement of the various resonances. Entangled light can resolve certain states even when strong background due to fast dephasing suppresses the resonant features when probed by classical light.

We theoretically investigate exciton relaxation dynamics in molecular aggregates based on model photosynthetic complexes under various conditions of incoherent excitation. We show that noise-induced quantum coherence is generated between spatially-separated exciton states which belong to the same or different energy transfer pathways, coupled via real and virtual transfer processes. Such quantum coherence effects may be used to improve light-harvesting efficiency and to reveal quantum phenomena in biology., Comment: needs major revision

Excited-state vibrational dynamics in molecules can be studied by an electronically off-resonant Raman process induced by a probe pulse with variable delay with respect to an actinic pulse. We establish the connection between several variants of the technique that involve either spontaneous or stimulated Raman detection and different pulse configurations. By using loop diagrams in the frequency domain we show that all signals can be described as six wave mixing which depend on the same four point molecular correlation functions involving two transition dipoles and two polarizabilities and accompanied by a different gating. Simulations for the stochastic two-state-jump model illustrate the origin of the absorptive and dispersive features observed experimentally.

We calculate the third order susceptibility $\chi^{(3)}$ of a pair of 2 level atoms which interact via the exchange of photons. QED corrections to second order in coupling to vacuum field modes yield collective two photon absorption resonances which can be observed in transmission spectroscopy of shaped broadband pulses. While some collective effects can be obtained by introducing an effective interatomic coupling using a quantum master equation, the predicted signals contain clear features that are missed by that level of theory and require a full diagrammatic QED treatment.

Vibrational motions in electronically excited states can be observed by either time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both signals. Three representations for the signal which suggest different simulation protocols are developed. These are based on the forward and the backward propagation of the wavefunction, sum over state expansion using an effective vibration Hamiltonian and a semiclassical treatment of a bath. We show that the effective temporal ($\Delta t$) and spectral ($\Delta\omega$) resolution of the techniques is not controlled solely by experimental knobs but also depends on the system dynamics being probed. The Fourier uncertainty $\Delta\omega\Delta t>1$ is never violated.

The time-and-frequency resolved nonlinear light scattering (NLS) signals from a time evolving charge distribution of valence electrons prepared by impulsive X-ray pulses are calculated using a superoperator Green's function formalism. The signal consists of a coherent $\sim N^2$-scaling difference frequency generation and an incoherent fluorescence $\sim N$-scaling component where $N$ is the number of active molecules. The former is given by the classical Larmor formula based on the time-dependent charge density. The latter requires additional information about the electronic structure and may be recast in terms of transition amplitudes representing quantum matter pathways.

We investigate surface plasmon amplification in a silver nanoparticle coupled to an externally driven three-level gain medium, and show that quantum coherence significantly enhances the generation of surface plasmons. Surface plasmon amplification by stimulated emission of radiation is achieved in the absence of population inversion on the spasing transition, which reduces the pump requirements. The coherent drive allows us to control the dynamics, and holds promise for quantum control of nanoplasmonic devices., Comment: 5 pages, 4 figures

The non-classical spectral and temporal features of entangled photons offer new possibilities to investigate the interactions of excitons in photosynthetic complexes, and to target the excitation of specific states. Simulations of fluorescence in the bacterial reaction center induced by entangled light demonstrate a selectivity of double-exciton states which is not possible using classical stochastic light with the same power spectrum., Comment: 11 pages, 13 figures, published version

Ultralow-power diode-laser radiation is employed to induce photodesorption of cesium from a partially transparent thin-film cesium adsorbate on a solid surface. Using resonant Raman spectroscopy, we demonstrate that this photodesorption process enables an accurate local optical control of the density of dimer molecules in alkali-metal vapors., Comment: 4 pages, 4 figures

In this work we report a quantum interference mediated control of the resonance profiles in a generic three-level system and investigate its effect on key quantum interference (QI) phenomena. Namely in a three level configuration with doublets in the ground or excited states, we show control over enhancement and suppression of the emission (absorption) profiles. This is achieved by manipulation of the strength of QI and the energy spacing of the doublets. We analyze the application of such QI induced control of the resonance profile in the framework of two limiting cases of lasing without inversion and photo-detection., Comment: 8 pages, 5 figures

We show that quantum coherence can increase the quantum efficiency of various thermodynamic systems. For example, we can enhance the quantum efficiency for a quantum dot photocell, a laser based solar cell and the photo-Carnot quantum heat engine. Our results are fully consistent with the laws of thermodynamics contrary to comments found in the paper of A.P. Kirk, Phys. Rev. Lett. 106, 048703 (2011)., Comment: 11 pages, 6 figures