Density Matrix Research Articles

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Kylin-V: An open-source package calculating the dynamic and spectroscopic properties of large systems.

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples.

Muonium state exchange dynamics in n -type GaAs

Muonium (Mu), a pseudoisotope of hydrogen with a positively charged muon in place of the proton, takes the form Mu+,0,− (like isolated hydrogen, i.e., H+,0,−) in semiconductors. The specifics of the charge state depend on the local electronic environment of the host. After initial muon implantation, generated Mu centers interact with free charge carriers and electronic spins, transition between sites, and form a dynamic network of state exchange. We identified the model of Mu dynamics in n-type GaAs using the density matrix simulation method and photoexcited muon spin spectroscopy technique. Fitting to the dark and illuminated μSR data provided transition rates between Mu states, revealing the underlying mechanisms at play between the Mu centers (cf. isolated H) and the host. Deduced capture/scattering cross sections of the Mu states reflected the microscopic dynamics of Mu. Illumination studies enabled us to measure interactions between Mu and minority carriers, which would be unavailable in dark measurements without heating. The methodology developed in this study may be applied to other semiconductor systems for a deeper understanding of the Mu state exchange dynamics. Published by the American Physical Society 2024

Analysis of the nonlinear optical properties, vibrational spectra, DFT method and photovoltaic performance of cyanidin-3-rutinoside chloride

This study aims to identify a cyanidin-3-rutinoside chloride that exhibits both photovoltaic performance and nonlinear optical properties, which may be utilized in the field of optoelectronics. Prior to investigating these properties, the stable structure must be determined. For this purpose, its conformational analysis is performed by the Molecular Force Field method with the spartan program. The exact nature of the stable configuration has been ascertained by empirical evidence. The energy of the stable configuration is -1654184.76 kcal/mol, and its dipole moment is 9.94 Debye. Cyanidin-3-rutinoside chloride has been investigated using experimental FT-IR and Raman spectroscopies. Meanwhile, the DFT method at the B3LYP/6-311 + + G(d, p) level was employed in order to study the simulated FT-IR and Raman spectra, the HOMO-LUMO analysis, the molecular electrostatic potentials (MEP), and the non-linear optical (NLO) characteristics of the title molecule. The HOMO and LUMO energies are − 6.45 and − 3.64 electron volts (eV), respectively, with a gap value of 2.81 eV. Additionally, the title compound’s open-circuit voltage, the transition density matrix light-harvesting efficiency, driving force, and binding energy were calculated with by taking photovoltaic cell properties into account. Furthermore, investigations of hole reorganization energy, electron reorganization energy, and total reorganization energy were carried out at the B3LYP/6-31G(d, p) level for the cyanidin-3-rutinoside chloride of interest. In addition, density of state calculations and NBO were made at the B3LYP/6-31G(d, p) level. We calculated the following values for LHE, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{V}_{oc}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{{\\Delta\\:}\ ext{G}}_{\ ext{i}\ ext{n}\ ext{j}\ ext{e}\ ext{c}\ ext{t}}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{E}_{b}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\lambda\\:}_{h}$$\\end{document}, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\lambda\\:}_{e}$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\lambda\\:}_{total}$$\\end{document} : 0.06, 2.45 eV, 0.20 eV, 0.56 eV, 0.50 eV, 0.57 eV and 1.06 eV, respectively.

Witness of non-Markovian dynamics based on Bhattacharyya quantum distance

Non-Markovian effects due to quantum memory in the dynamics of open systems typically correspond to information backflows from the surrounding environment to the system. We propose a witness to quantify the non-Markovianity of quantum evolutions using the Bhattacharyya distance (BD), a specific quantum statistical distance. This witness has the advantage of not requiring the calculation of the evolved density matrix and only computes through the initial and final states of the system, therefore leading to the improvement of quantum metrology. It means that we calculate the quantum angle between two states to detect non-Markovian effects. This proposal is investigated by considering several instances of open quantum systems, such as two and three-level atoms interacting in single and two-mode fields, respectively, and two effective two-level atoms interacting locally with two independent environments. We demonstrate that the suggested BD-based non-Markovianity witness identifies memory effects, consistent with well-established witnesses based on Bures distance, quantum Fisher information, and Hilbert-Schmidt speed, showing sensitivity to information backflows.

Strong-coupling quantum thermodynamics of quantum Brownian motion based on the exact solution of its reduced density matrix

Strong-coupling quantum thermodynamics of quantum Brownian motion based on the exact solution of its reduced density matrix

Reduced Density Matrix Formulation of Quantum Linear Response.

The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photoinduced processes in molecular systems. With the advances of quantum computing, we recently adapted this method for near-term quantum hardware using a truncated active space approximation with orbital rotation, named quantum linear response (qLR). In an effort to reduce the classic cost of this hybrid approach, we here derive and implement a reduced density matrix (RDM) driven approach of qLR. This allows for the calculation of spectral properties of moderately sized molecules with much larger basis sets than so far possible. We report qLR results for benzene and R-methyloxirane with a cc-pVTZ basis set and study the effect of shot noise on the valence and oxygen K-edge absorption spectra of H2O in the cc-pVTZ basis.

Calculating Molecular Polarizabilities Using Exact Frozen Density Embedding with External Orthogonality.

Frozen density embedding (FDE) with freeze-thaw cycles is a formally exact embedding scheme. In practice, this method is limited to systems with small density overlaps when approximate nonadditive kinetic energy functionals are used. It has been shown that the use of approximate nonadditive kinetic energy functionals can be avoided when external orthogonality (EO) is enforced, and FDE can then generate exact results even for strongly overlapping subsystems. In this work, we present an implementation of exact FDEc-EO (coupled FDE TDDFT with EO) for the calculation of polarizabilities in the Amsterdam density functional program package. EO is enforced using the level-shift projection operator method, which ensures that orbitals between fragments are orthogonal. For pure functionals, we show that only the symmetric EO contributions to the induced density matrix are needed. This leads to a simplified implementation for the calculation of polarizability that can exactly reproduce the supermolecular TDDFT results. We further discuss the limitation of exact FDEc-EO in interpreting subsystem polarizabilities due to the nonunique partitioning of the total density. We show that this limitation is due to the fact that subsystem polarizability partitioning is dependent on how the subsystems are initially polarized. As supermolecular virtual orbitals are exactly reproduced, this dependence is attributed to the description of the occupied orbitals. In contrast, for excitations of subsystems that are localized within one subsystem, we show that the excitation energies are stable with respect to the order of polarization. This observation shows that impacts from the nonunique nature of exact FDE on subsystem properties can be minimized by better fragmentation of the supermolecular systems if the property is localized. For global properties like polarizability, this is not the case, and nonuniqueness remains independent of the fragmentation used.

Quantum modeling simulates nutrient effect of bioplastic polyhydroxyalkanoate (PHA) production in Pseudomonas putida

Polyhydroxyalkanoates (PHAs) could be used to make sustainable, biodegradable plastics. However, the precise and accurate mechanistic modeling of PHA biosynthesis, especially medium-chain-length PHA (mcl-PHA), for yield improvement remains a challenge to biology. PHA biosynthesis is typically triggered by nitrogen limitation and tends to peak at an optimal carbon-to-nitrogen (C/N) ratio. Specifically, simulation of the underlying dynamic regulation mechanisms for PHA bioprocess is a bottleneck owing to surfeit model complexity and current modeling philosophies for uncertainty. To address this issue, we proposed a quantum-like decision-making model to encode gene expression and regulation events as hidden layers by the general transformation of a density matrix, which uses the interference of probability amplitudes to provide an empirical-level description for PHA biosynthesis. We implemented our framework modeling the biosynthesis of mcl-PHA in Pseudomonas putida with respect to external C/N ratios, showing its optimization production at maximum PHA production of 13.81% cell dry mass (CDM) at the C/N ratio of 40:1. The results also suggest the degree of P. putida’s preference in channeling carbon towards PHA production as part of the bacterium’s adaptative behavior to nutrient stress using quantum formalism. Generic parameters (kD, kN and theta θ) obtained based on such quantum formulation, representing P. putida’s PHA biosynthesis with respect to external C/N ratios, was discussed. This work offers a new perspective on the use of quantum theory for PHA production, demonstrating its application potential for other bioprocesses.

Effects of hydrostatic pressure, temperature, and position-dependent mass on the nonlinear optical properties of triple delta-doped GaAs quantum well

In this study, we thoroughly investigate the impacts of hydrostatic pressure, temperature, and position-dependent mass (PDM) on the nonlinear optical properties of asymmetric triple δ-doped GaAs quantum wells. Our analysis covers total optical absorption coefficients, relative refractive index changes, nonlinear optical rectification, second harmonic generation, and third harmonic generation. Initially, we employ PDM to solve the time-independent Schrödinger equation using the diagonalization method under effective mass and parabolic band approaches, considering pressure and temperature dependencies. Utilizing the first four energy eigenvalues and eigenfunctions, we apply the compact density matrix method to compute the system’s nonlinear optical properties numerically. The results indicate a shift in optical property peak positions toward lower (higher) energy spectra with increasing hydrostatic pressure (temperature). Furthermore, the influence of PDM shifts the system’s optical properties toward the higher energy spectrum, resembling the effect of temperature. From an experimental and theoretical perspective, one of the topics that researchers work on most is GaAs-based δ-doped systems (δ-doped heterojunction bipolar transistors, δ-doped field effect transistors, δ-multiple independent gate field effect transistors, etc.). We believe these findings will provide valuable insights for the researchers involved in GaAs-based δ-doped optoelectronic device design.

The Spatiotemporal Doubled‐Density Operator: A Unified Framework for Analyzing Spatial and Temporal Quantum Processes

AbstractThe measurement statistics for spatial and temporal quantum processes are produced through distinct mechanisms. Measurements that are space‐like separated exhibit non‐signaling behavior. However, time‐like separated measurements can only result in one‐way non‐signaling, as the past is independent of the future, but the opposite is not true. This work presents the doubled‐density operator as a comprehensive framework for studying quantum processes in space‐time. It effectively captures all the physical information of the process, with the measurement and Born rule showing uniformity for both spatial and temporal cases. It is demonstrated that the equal‐time density operator can be derived by performing a partial trace operation on the doubled‐density operator. Furthermore, the temporality of the quantum process can be detected by conducting a partial trace operation on either the left or right half of the doubled‐density operator.

Theoretical investigation of optoelectronic properties in PbS/CdS core/shell spherical quantum dots under the effect of the electric field intensity, hydrogenic impurity and geometric parameters

In this paper, we theoretically investigated the combined effects of the external electric field (EF) strength and the geometric parameters on the linear, nonlinear and total dielectric functions as well as the effective dielectric function (DF) coefficients of PbS/CdS spherical core/shell quantum dots (CSQD) in the presence of the hydrogenic impurity located at the center. The subband energy eigenvalues and their corresponding wave functions are obtained by solving the time-independent Schrödinger equation and using the variational method (VM) in the framework of the effective mass approximation (EMA). The linear, nonlinear and total DF as well as the effective DF were discussed and evaluated under the influence of EF intensity, geometric parameters, the change of the number of quantum dots (QDs) per unit volume and optical intensity I based on the compact density matrix (CDM) approach. The obtained results show that the height peaks of the linear, nonlinear and Total DF as well as the effective DF coefficients increase and their resonant peak moves towards lower energies as the EF and geometric factors increase in both cases with and without considering the hydrogenic impurity effect. Furthermore, our findings show that the impact of optical intensity and the number of QDs per unit volume does not change the resonance peaks of imaginary parts of DF and effective DF but decreases their magnitudes. As a result, we believe that numerical results will present important developments and provide great contributions in designing new optoelectronic devices related to CSQD hetero-nanostructure.

Role of electron withdrawing moieties in phenoxazine–oxadiazole-based donor–acceptor compounds towards enriching TADF emission

Herein, we reported the effect of electron withdrawing units, such as trifluoromethyl (CF3) and cyanide (CN), substitution on a thermally activated delayed fluorescent (TADF) molecule (10-(4-(5-phenyl-1,3,4-oxadiazol-2-yl)phenyl)-10H-phenoxazine (PXZ-OXD)). The addition of electron withdrawing units has increased the acceptor strength and reduced the interaction between PXZ and OXD, thus reducing the gap between the singlet and triplet states (ΔEST) of excitons. To understand the variation in the acceptor strength of PXZ-OXD as a function of its molecular structure and density of states, density functional theory (DFT) and time-dependent DFT (TDDFT) were conducted. Transition density matrix investigations revealed that the addition of −CF3 and –CN to PXZ-OXD triggers CT excitons, while inducing lower ΔEST values. Particularly, the lowest ΔEST (0.05 eV) with a notable red shift in the emission spectrum was observed with 4′-CF3PXZOXD. The delayed component lifetime of PXZOXD is found to be reduced after the substitution of −CNwhm and −CF3. Despite the weak charge transfer transitions, the substitution of conjugative –CN group is found to be beneficial in improving the HOMO-LUMO overlap with a moderate decrease in reverse intersystem crossing (KRISC), which attained enhancement in the photoluminescent quantum yield. Additionally, the substitution of the above electron withdrawing units on PXZ-OXD yielded a red shift in the electroluminescence spectrum. Furthermore, the external quantum efficiency (at 100 cd/m2, i.e., EQE100) of the 4′-CNPXZOXD-based organic light-emitting diode is found to improve by 21.13 % against the PXZOXD (16.9 %).

A formulation of quantum fluid mechanics and trajectories

A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent Schrödinger equation, respectively, where the Schrödinger equation is in density matrix form. For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations of fluid mechanics, respectively. Generalizations of the energy and Euler equations are derived to obtain equations that are in the same form as they are in classical mechanics. The fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local variable mass. Over all space mass is conserved. The variable mass is a necessary condition for the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross flows are examined, where velocity directions are changed without changing the kinetic energy. For one-electron atoms, the velocity modification gives closed orbits for trajectories, and mass conservation, vortexes, and density stratification for fluid flows. For many body states, under certain conditions, and by hypotheses, Euler equations of orbital-flows are obtained. One-body Schrödinger equations that are a generalization of the Hartree–Fock equations are also obtained. These equations contain a quantum Coulomb’s law, involving the 2-body pair function of reduced density matrix theory that replace the charge densities.

TD-DMRG Study of Exciton Dynamics with both Thermal and Static Disorders for Fenna-Matthews-Olson Complex.

Photosynthesis is a fundamental process that converts solar energy into chemical energy. Understanding the microscopic mechanisms of energy transfer in photosynthetic systems is crucial for the development of novel optoelectronic materials. Simulating these processes poses significant challenges due to the intricate interactions between electrons and phonons, compounded by static disorder. In this work, we present a numerically nearly exact study using the time-dependent density matrix renormalization group (TD-DMRG) method to simulate the quantum dynamics of the Fenna-Matthews-Olson (FMO) complex considering an eight-site model with both thermal and static disorders. We employ the thermo-field dynamics formalism for temperature effects. We merge all electronic interactions into one large matrix product state (MPS) site, boosting accuracy efficiently without increasing complexity. Previous combined experimental and computational studies indicated that the static disorders range from 30 to 90 cm-1 for different FMO sites. We employ a Gaussian distribution and the auxiliary bosonic operator approach to consider the static disorder in our TD-DMRG algorithm. We investigate the impact of different initial excitation sites, temperatures, and degrees of static disorder on the exciton dynamics and temporal coherence. It is found that under the influence of the experimentally determined static disorder strength, the exciton population evolution shows a non-negligible difference at zero temperature, while it is hardly affected at room temperature.

Note on quantum discord

Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit-qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.

Optical absorption properties in multi-layer InGaN/GaN core-shell quantum dots: The influences of ternary mixed crystal effect and hydrogen-like impurity

Based on the effective mass approximation and the compact density matrix theory, the electronic states and optical absorption properties of intersubband transitions between the conduction-band energy levels in zinc-blende InGaN/GaN/InGaN/GaN core-shell quantum dots (CSQDs) are investigated by using the finite difference method. The effects of hydrogen-like impurity and In component on the wave functions, transition energies, and optical absorption properties are discussed in detail. The results show that hydrogen-like impurity can cause the peak positions of optical absorption coefficients (OACs) and refractive index changes (RICs) to move to high energy area, and the peak values of OACs rise. Increasing In component of InGaN crystal in the core region of a CSQD has the same effect. But an opposite tendency will be found when increasing In component in the shell-well of a CSQD, i.e. optical absorption peaks move to low energy area and their values decrease. Comparing to the shell-well, the core region has more powerful confinement effect on electrons. So the better absorption properties are more likely to be obtained for this type of multi-layer InGaN/GaN CSQDs when In component in the core is larger than that in the shell-well.

On accurate calculations of equilibrium H/D fractionations at super-cold conditions (≤200 K) I: Full Partition Function Ratio (FPFR) vs. Path Integral Monte Carlo (PIMC)

Accurate estimations of Hydrogen/Deuterium (H/D) isotope effects have been a long-standing problem since the beginning of stable isotope geochemistry, primarily due to their strong nuclear quantum effects (NQEs). Currently, the D/H ratio plays a key role in deciphering the origin and evolution of water ice and organics in the solar system. Additionally, the Big-bang origin of Deuterium necessitates that the observed D/H variations be linked to isotope exchange reactions, such as HD + H2O ↔ H2 + HDO. Therefore, an accurate benchmark dataset describing the equilibrium H/D isotope fractionations at low temperatures (≤ 200 K) is essential for interpreting rapidly accumulating astrochemical observation data. In this study, we implemented and compared two methods developed for evaluating the NQEs of H/D isotopes: 1) the Full Partition Function Ratio (FPFR) method and 2) the Path-Integral Monte Carlo (PIMC) method. Both were assessed for their accuracy and efficiency in estimating equilibrium isotope effects (EIEs) using 10 common interstellar small molecules (H2, HF, HCl, HCN, HNC, H2O, H2S, NH3, HCHO, and CH4) as examples. Most of them are calculated at high precision for the first time. For the FPFR method, several higher-order corrections to the Urey-Bigeleisen-Mayer model were considered, including anharmonicity, quantum-mechanical rotation with nuclear-spin statistics, and corrections to the Born-Oppenheimer approximation. For the PIMC method, four different actions related to the thermal density matrix are used. These include the primitive and three fourth-order actions (Takahashi and Imada, Suzuki-Chin and Chin approximations), based on the direct scaled-coordinates transformation. Three main conclusions are obtained: 1) Under the framework of Born-Oppenheimer approximation, the PIMC method holds the same and even slightly better accuracy (more comprehensive descriptions of quantum anharmonicities) in estimating EIEs for H/D isotopes as the FPFR method. However, both methods suffer from the neglection of the DBOC when using the Born-Oppenheimer potential energy surfaces. For the PIMC method, additional corrections for particle distinguishability must be considered when nuclear spin statistics exhibit its effects at low temperatures (e.g., < 160 K for H2). 2) Among the four actions, three fourth-order actions show better convergence and efficiency (2.2 to 26.5 times speedups at 50 K) than the primitive action, making them superior candidates for PIMC simulations at super-cold (≤ 200 K) conditions. 3) A combination of accurate potential energy surface with the PIMC method serves as an alternative way for theoretical estimations of H/D isotope effects.

Accelerating and breaking adaptive nano-colloids (

Unlike conventional colloids showing random mobility because of Brownian motion, active colloids contain nanomotors that translate chemical or physical triggers into directed movement. Whereas the acceleration of such particles works well, it is difficult to decelerate them by request. Compared to the existing literature on microscaled swimmers/robots, the main question of the current paper is whether nanoscaled colloids (<100 nm) can also be actively controlled despite the stronger relevance of rotational diffusion at such dimensions. We developed nanoparticles comprising two independent mechanisms for propulsion: a chemical engine associated with a Janus-type modification of organosilica nanoparticles and physical locomotion because of a superparamagnetic core inside these particles. Both triggers can be used independently to initiate the particles' directed and anisotropic movement. The magnetic forces can be tuned, most importantly concerning the angle defining the chemical acceleration. Superposition and a boost state are adopted for a parallel alignment. However, when the magnetic field acting on the particles is turned to an antiparallel orientation, a rapid deceleration can be observed, and the colloids halt.

Experimental demonstration of quantum encryption in phase space with displacement operator in coherent optical communications

We provide experimental validation of quantum encryption in phase space using displacement operators in coherent states (DOCS) in a conventional coherent optical communication system. The proposed encryption technique is based on displacing the information symbols in the phase space using random phases and amplitudes to achieve encryption randomly and provide security at the physical layer. We also introduce a dual polarization encryption approach where we use two different and random DOCS to encrypt the X and Y polarizations separately. The experimental results show that only authorized users can decrypt the signal correctly, and any mismatch in the displacement operator coefficients, amplitudes, or phases will lead to a bit error ratio (BER) of approximately 50%. We also compare the performance of the system with and without encryption over 80 km of standard-single mode fiber (SSMF) transmission to assess the added penalty of such encryption. The achieved net bit rates are 224, 448, and 560 Gb/s for QPSK, 16QAM, and 32QAM modulation formats, respectively. The experimental results showcase the efficacy of the DOCS encryption technique in resisting various decryption attempts, demonstrating its effectiveness in ensuring the security and confidentiality of transmitted data in a real-world transmission scenario.