Conventional 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. This Roadmap article focuses on using quantum light as a powerful sensing and spectroscopic tool to reveal novel information about complex molecules that is not accessible by classical light. It aims at bridging the quantum optics and spectroscopy communities which normally have opposite goals: manipulating complex light states with simple matter e.g. qubits vs. studying complex molecules with simple classical light, respectively. Articles cover advances in the generation and manipulation of state-of-the-art quantum light sources along with applications to sensing, spectroscopy, imaging and interferometry.

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett., 101 , 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional nopumping theorem.PACS numbers: 03.65.Vf,05.10.Gg , Molecular motors and machines are an essential component in living organisms. They perform tasks such as carrying loads, contracting muscles and many other crucial functions [1]. Many research groups are actively trying to venture beyond the motors found in nature, aiming to design and synthesize artificial molecular machines [2][3][4][5][6].Since artificial machines can be designed, it is possible to operate them using new driving mechanisms which are not found in biological motors and machines. One such driving mechanism is the rectification of periodic time variation of external parameters. Due to the similarity with everyday pumps such systems are often referred to as stochastic pumps. Stochastic pumps are therefore closely related to thermal ratchets [7], but the term is more commonly used for systems with a discrete set of coarse-grained states. The dynamics of stochastic pumps have been investigated extensively in recent years [8][9][10][11][12][13], see also the reviews by Sinitsyn [14] and Astumian [15] for an overview.Motivated by a beautiful experiment on catananes [16], and by work focused on an adiabatically driven model [17], a no-pumping theorem (NPT) for stochastic pumps was found [18]. This non adiabatic result identifies driving mechanisms which will not lead to directed motion. In a parallel development, Chernyak and Sinitsyn [19] showed how to generalize the NPT to account for the topology of the network of transitions between states. Due to its simple structure, and somewhat non intuitive result, the NPT has generated considerable interest [20][21][22][23][24]. All this body of work was focused on the stochastic dynamics of a single particle. The aim of this letter is to investigate the validity of the NPT for many particle stochastic pumps, where several interacting particles jump between a set of binding sites. We demonstrate that an NPT holds for this many particle system for any local interaction.Single particle NPT-Consider a system which makes sudden transitions between a set of coarse-grained states, labeled by α, β, γ, · · · The transition are assumed to be Markovian and are characterized by transition ratesThe graph representation of stochastic pumps with 4 sites and 5 bidirectional transitions: (a) the single particle pump, (b) and (c) the product graph representing a system with 2 and 3 particles respectively. The nodes of the product graphs correspond to many particle states such as (α, γ, α).R βα ≥ 0 (for α = β). We assume that the system is connected,...

A twisted X-ray beam with orbital angular momentum is employed in a theoretical study to probe molecular chirality. A nonlocal response description of the matter-field coupling is adopted to account for the field short wavelength and the structured spatial profile. We use the minimal-coupling Hamiltonian, which implicitly takes into account the multipole contributions to all orders. The combined interactions of the spin and orbital angular momentum of the X-ray beam give rise to circular-helical dichroism signals, which are stronger than ordinary circular dichroism signals, and may serve as a useful tool for the study of molecular chirality in the X-ray regime.

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 ∝ I 1/2 p , where Ip is the source intensity, compared to ∝ Ip 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.Rapid advances in short-wavelength ultrafast light sources, have revolutionized our ability to observe the microscopic world. With bright Free Electron Lasers and high harmonics tabletop sources, short time (femtosecond) and length (subnanometer) scales become accessible experimentally. These offer new exciting possibilities to study spatio-spectral properties of quantum systems driven out of equilibrium, and monitor dynamical relaxation processes and chemical reactions. The spatial features of small-scale charge distributions can be recorded in time. Far-field off-resonant X-ray diffraction measurements provide useful information on the charge density σ (Q) where Q is the diffraction wavector. The observed diffraction pattern S (Q) is given by the modulus square S (Q) ∝ |σ (Q)| 2 . Inverting these signals to real-space σ (r) requires a Fourier transform. Since the phase of σ (Q) is not available, the inversion requires phase retrieval which can be done using either algorithmic solutions [1,2] or more sophisticated and costly experimental setups such as heterodyne measurements [3]. Correlated beam techniques [4][5][6][7][8][9][10] in the visible regime, have been shown to circumvent this problem by producing the realspace image of mesoscopic objects. Such techniques have classical analogues using correlated light, and reveal the modulus square of the studied object |σ (r)| 2 [11,12]. In this paper we consider the setup shown in Fig.(1). We focus on off-resonant scattering of entangled photons in which only one photon, denoted as the "signal", interacts with a sample. Its entangled counterpart, the "idler", is spatially scanned and measured in coincidence with the arrival of the signal photon. The idler reveals the image and also uncovers phase information, as was recently shown in [13] for linear diffraction.Our first main result is that for small diffraction angles, using Schmidt decomposition of the two-photon amplitude Φ (q s , q i ) = ∞ n √ λ n u n (q s ) v n (q i ) where λ n is the respective mode weight -reads,Here β(1) nm = dr u n (r) σ (r) u * m (r), β(2) nm = dr u n (r) |σ (r)| 2 u * m (r) andρ i represents the transverse detection plane. σ (r) is the charge density of the target object prepared by an actinic pulse and p = (1...

Entangled photon pairs have been used for molecular spectroscopy in the form of entangled two-photon absorption and in quantum interferometry for precise measurements of light source properties and time delays. We present an experiment that combines molecular spectroscopy and quantum interferometry by utilizing the correlations of entangled photons in a Hong−Ou−Mandel (HOM) interferometer to study molecular properties. We find that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer, and the resulting signal contains information pertaining to the light−matter interaction. We can extract the dephasing time of the coherent response induced by the excitation on a femtosecond time scale. A dephasing time of 102 fs is obtained, which is relatively short compared to times found with similar methods and considering line width broadening and the instrument entanglement time As the measurement is done with coincidence counts as opposed to simply intensity, it is unaffected by even-order dispersion effects, and because interactions with the molecular state affect the photon correlation, the observed measurement contains only these effects and no other classical losses. The experiments are accompanied by theory that predicts the observed temporal shift and captures the entangled photon joint spectral amplitude and the molecule's transmission in the coincidence counting rate. Thus, we present a proof-of-concept experimental method based of entangled photon interferometry that can be used to characterize optical properties in organic molecules and can in the future be expanded on for more complex spectroscopic studies of nonlinear optical properties.