The measurement of circular dichroism (CD) has widely been exploited to distinguish the different enantiomers of chiral structures. It has been applied to natural materials (e.g., molecules) as well as to artificial materials (e.g., nanophotonic structures). However, especially for chiral molecules the signal level is very low and increasing the signal-to-noise ratio is of paramount importance to either shorten the necessary measurement time or to lower the minimum detectable molecule concentration. As one solution to this problem, we propose here to use quantum states of light in CD sensing to reduce the noise below the shot noise level encountered when using coherent states of light. Through a multiparameter estimation approach, we identify the ultimate quantum limit of the precision in CD sensing, allowing for general schemes including additional ancillary modes. We show that the ultimate quantum limit can be achieved by various optimal schemes. These include using a pair of Fock-state probes in a direct sensing configuration and pairs of twin beams in an ancilla-assisted sensing configuration, for both of which photon number-resolved detection is shown to be the optimal measurement. These optimal schemes offer a significant quantum enhancement even in the presence of some additional system loss. The near optimality of a scheme using a single twin beam in a direct sensing configuration is also shown for cases where the actual CD signal is very small. Alternative optimal schemes involving single-photon sources and detectors are also proposed. This work paves the way for further investigations of quantum metrological techniques in chirality sensing.
The measurement of circular dichroism (CD) has widely been exploited to distinguish the different enantiomers of chiral structures. It has been applied to natural materials (e.g., molecules) as well as to artificial materials (e.g., nanophotonic structures). However, especially for chiral molecules the signal level is very low and increasing the signal-to-noise ratio is of paramount importance to either shorten the necessary measurement time or to lower the minimum detectable molecule concentration. As one solution to this problem, we propose here to use quantum states of light in CD sensing to reduce the noise below the shot noise level encountered when using coherent states of light. Through a multiparameter estimation approach, we identify the ultimate quantum limit of the precision in CD sensing, allowing for general schemes including additional ancillary modes. We show that the ultimate quantum limit can be achieved by various optimal schemes. These include using a pair of Fock-state probes in a direct sensing configuration and pairs of twin beams in an ancilla-assisted sensing configuration, for both of which photon number-resolved detection is shown to be the optimal measurement. These optimal schemes offer a significant quantum enhancement even in the presence of some additional system loss. The near optimality of a scheme using a single twin beam in a direct sensing configuration is also shown for cases where the actual CD signal is very small. Alternative optimal schemes involving single-photon sources and detectors are also proposed. This work paves the way for further investigations of quantum metrological techniques in chirality sensing.
Circular dichroism is a widely used technique for investigating optically chiral molecules, especially for biomolecules. It is thus of great importance that these parameters be estimated precisely so that the molecules with desired functionalities can be designed. In order to surpass the limits of classical measurements, we need to probe the system with quantum light. We develop the quantum Fisher information matrix (QFIM) for precision estimates of the circular dichroism and the optical rotary dispersion for a variety of input quantum states of light that are easily accessible in the laboratory. The Cramer-Rao bounds for all four chirality parameters are obtained from the QFIM for (a) single photon input states with a specific linear polarization and for (b) NOON states having two photons with both either left polarized or right polarized. The QFIM bounds, using quantum light, are compared with bounds obtained for classical light beams, i.e., beams in coherent states. Quite generally, both the single-photon state and the NOON state exhibit superior precision in the estimation of absorption and phase shift in relation to a coherent source of comparable intensity, especially in the weak-absorption regime. In particular, the NOON state naturally offers the best precision among the three. We compare QFIM bounds with the error sensitivity bounds, as the latter are relatively easier to measure whereas the QFIM bounds require full state tomography.
In recent times there has been growing interest in Raman optical activity (ROA) for its label free detection of absolute configuration, conformation, and stereochemical structure in chiral biosamples and drug molecules. Since ROA signals are generally small, techniques such as stimulation by a probe beam can be used to enhance the signal strength. However, with a classical probe, the measurement precision is still fundamentally limited by its shot noise. To solve this problem we propose the use of two-mode squeezed vacuum and show that it can achieve sub-shot noise limited measurement sensitivity. Using quantum estimation theory, we derived the quantum Fisher information and the quantum Cramér-Rao bound (QCRB) for stimulated ROA measurement to quantify the precision enhancement. This improvement comes from photon-number correlations which suppress the intensity fluctuation common to both modes. We further show that balanced detection of the output intensity difference is a practical measurement scheme that approaches the QCRB and becomes optimal in the small-chirality limit. This opens a promising path toward more sensitive Raman chiroptical spectroscopy of weak and photosensitive samples.
Circular dichroism (CD), which detects differential absorption with left- and right-circularly polarized light, is widely used for characterizing molecular chirality. Despite its similarity to absorption spectroscopy, CD spectroscopy typically requires a significantly longer time to acquire a spectrum due to the low intensity of the CD signal. The CD measurements can be accelerated if the noise level in the spectra can be reduced, which facilitates the detection of the weak CD signal. Here we show that such noise suppression is indeed possible using entangled photon pairs as the light source. By taking advantage of the photon number correlation of entangled photon pairs, we suppressed the noise contained in the CD spectra by 30% below the shot-noise limit which is a fundamental limit in conventional CD measurements. As a consequence, sub-shot-noise CD spectroscopy developed in this study is capable of characterizing the molecular chirality twice as fast as conventional CD spectroscopy.
Circular dichroism (CD) spectrum and optical rotation (OR) spectrum, crucial for understanding molecular properties and configurations, present challenges due to limited testing methods and equipment accuracy in the ultraviolet (UV) region. This study proposes a weak measurement system for chiral signals in varying concentrations in the ultraviolet range, optimized using a deep neural network (DNN) model. Introducing different post-selections to detect the circular dichroism spectrum and optical rotation spectrum separately, with contrast as a probe, it achieves a detection resolution of up to 10 −6 rad. Moreover, the fitted value of the training data can reach 0.9989, enhancing the prediction accuracy of chiral molecule concentrations. This method exhibits considerable promise for applications in chiral measurement and sensor technologies.
The most important problem of spectroscopic chiral analysis is the enantioselective effects of the light-molecule interactions are inherently weak and severely reduced by the environment noises. Enormous efforts had been spent to overcome this problem by enhancing the symmetry break in the light-molecule interactions or reducing the environment noises. Here, we propose an alternative way to solve this problem by using frequency-entangled two-photon pairs as probe signals and detecting them in coincidence, i.e., using quantum chiral spectroscopy. For this purpose, we develop the theory of entanglement-assisted quantum chiral spectroscopy. Our results show that the quantum spectra of the left- and right-handed molecules are always distinguishable by suitably configuring the frequency-entangled two-photon pairs. In contrast, the classical spectra of the two enantiomers, where the broadband signal photon is frequency-uncorrelated with the idle one, become indistinguishable in the strong dissipation region. This offers our quantum chiral spectroscopy a great advantage over the classical chiral spectroscopy. Our work opens up an exciting area that exploring profound advantages of the quantum spectroscopy in chiral analysis.
The characterization of electric and magnetic dipole moments (EDM and MDM) in quantum systems is central to fundamental physics and quantum sensing. While EDM searches provide powerful probes of CP violation within and beyond the Standard Model, precise MDM estimation is crucial for high-precision magnetometry and the development of quantum sensors. In this work, we address the ultimate precision limits for separate and simultaneous estimation of both dipole moments in a generic two-level system coupled to electromagnetic fields. We analyze three classes of quantum probes/strategies: unitary and depolarizing dynamics, and thermal equilibrium states. For each, we derive the quantum Fisher information (matrix), identify optimal probes, and determine the ideal operating conditions, such as evolution times and temperatures, that maximize estimation precision. We further assess the compatibility and sloppiness of the statistical models, showing that orthogonal dipole moments configurations enable joint estimation of EDM and MDM, whereas parallel configurations are intrinsically sloppy, permitting only the estimation of a single parameter combination. Our results provide a unified metrological framework for estimation schemes ranging from neutron EDM searches to molecular magnetometry, and highlight the distinct roles of coherence, noise, and thermalization in multiparameter quantum sensing of dipole moments.