Hamiltonian Approximation Research Articles

Exploring entanglement dynamics in an optomechanical cavity with a type-[formula omitted] qutrit and quantized two-mode field

In this work, the main objective is to measure the degree of interaction of a type-V qutrit with a two-mode quantized field in an optomechanical cavity. To achieve this objective, we first deduce the Hamiltonian in the interaction picture to identify the oscillatory terms. Using the Coarse-Grained Method (CGM), we obtain the effective Hamiltonian analytically. By selecting initial conditions for the atom, the two-mode field, and the moving mirror, we can determine the state vector of the entire system through a first-order approximation of the effective Hamiltonian. With this information, we proceed to solve the Schrödinger equation, generating a coupled set of differential equations that is solved numerically based on the initial conditions. In this context, the atomic von Neumann entropy allows us to obtain the temporal evolution of the degree of entanglement of the qutrit in the cavity and the atomic population inversion. The results indicate that entanglement in this tripartite system, composed of the qutrit and the mirror-field subsystems, as well as the population inversion, can be manipulated by the initial state conditions of the system, the qutrit-field and mirror-field coupling coefficients, the pump field, and the dissipation rates of the two-mode field and the movable mirror, respectively.

Interband optical conductivity in electromagnetic field modulated strained black phosphorene

Black phosphorene (BP) has been widely investigated for its anisotropic and unique photoelectric properties. Strain, voltage and so on are commonly used to modulate the energy band structure and accordingly its photoelectric characteristics. In this study, we consider the energy band structure of BP in the vertical magnetic field, electric field, and in-plane/out-of-plane strains by using the tight-binding approximate Hamiltonian. The anisotropic frequency-dependent interband optical conductivity (IOC) of BP is investigated by using the Kubo formula in these modulation factors. Inherent asymmetry in band dispersion along the armchair (AC) direction and the zigzag (ZZ) direction leads to anisotropic IOC. The introduction of a vertical magnetic field induces band splitting, thereby generating multiple interband transition channels. In this case, the IOC along both the AC direction and the ZZ direction exhibits three peaks around the original peak position, and the magnitudes of the peaks are also modulated. With the increase of in-plane strain (from –20% to 20%), the band gap increases monotonically, and both the position and magnitude of the peaks vary with band gap changing. However, the band gap of BP undergoes a non-monotonic change under out-of-plane strain (from –20% to 20%), which is different from the change under in-plane strain. The band gap reaches a minimum value when a tensile strain of 12% is applied. Along the AC direction, the modulation of the IOC by in-plane strain is opposite to the modulation of out-of-plane strain (<i>ε</i><sub><i>z</i></sub> < 12%), indicating a competitive effect when triaxial strains are applied. Along the ZZ direction, in-plane strain primarily modulates the peak magnitude, while out-of-plane strain effectively modulates not only the peak position but also the peak magnitude obviously. The modulation of the IOC by forward and reverse electric fields are symmetrical. The coefficient for the peak position shift due to the vertical electric field is 1/2 in the AC direction and 1/10 in the ZZ direction. By integrating various modulation factors, we achieve versatile control over the energy band and IOC of BP, providing theoretical support for the application of BP in optoelectronic devices.

Insight on Gaussian Basis Set Truncation Errors in Weak to Intermediate Magnetic Fields with an Approximate Hamiltonian.

Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structures of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al., Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms 1 ≤ Z ≤ 18 in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from B = 0 to B = 0.6B0, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.

Guiding centre motion for particles in a ponderomotive magnetostatic end plug

The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.

Coordination of Mercury(II) in Water Promoted over Hydrolysis in Solvated Clusters [Hg(H2O)1-6](aq)2+: Insights from Relativistic Effects and Free Energy Analysis.

Understanding the nature of the interaction between mercury(II) ions, Hg2+, and water molecules is crucial to describe the stability and chemical behavior of structures formed during solvation, as well as the conditions that favor the Hg2+ coordination or inducing water hydrolysis. In our study, we explored exhaustively the potential energy surface of Hg2+ with up to six water molecules. We analyzed electronic and Gibbs free energies, binding, and nuclear magnetic resonance parameters. We used the zeroth-order regular approximation Hamiltonian, including scalar and spin-orbit relativistic corrections for free energy calculations and geometry optimizations to explore the interplay between electron correlation and relativistic effects. We analyzed intermolecular interactions with energy decomposition analysis, quantum theory of atoms in molecules, and natural bond orbital. Additionally, we used the four-component Dirac Hamiltonian to compute solvent effect on the magnetic shielding and J-coupling constants. Our results revealed that the water hydrolysis by Hg2+ requires a minimum of three water molecules. We found that the interaction between Hg2+ and water molecules is an orbital interaction due to relativistic effects and the most stable structures are opened-shape clusters, reducing the number of oxygen-mercury contacts and maximizing the formation of hydrogen bonds among water molecules. In these types of clusters, Hg2+ promotes the water hydrolysis over coordination with oxygen atoms. However, when we considered the change associated with the transfer of a cluster from the ideal gas to a solvated system, our solvation free energy analysis revealed that closed-shape clusters are more favorable, maximizing the number of oxygen-mercury contacts and reducing the formation of hydrogen bonds among water molecules. This finding suggests that, under room conditions, the coordination of Hg2+ is more favorable than hydrolysis. Our results have significant implications for understanding Hg2+ behavior in water, helping to develop targeted strategies for mercury remediation and management, and contributing to advancements in the broader field of environmental chemistry.

Bloch–Siegert Effect for Surface Nuclear Magnetic Resonance Sounding Experiments in the Unsaturated Zone

The Bloch–Siegert effect is relevant for NMR experiments where components of the excitation pulse other than the circularly polarized component have an influence on the evolution of the magnetization of the spin system under consideration. For linearly polarized excitation fields this happens at amplitudes higher than roughly one tenth of the magnitude of the static magnetic field. Since surface nuclear magnetic resonance (SNMR) experiments, also called magnetic-resonance-soundings (MRS), are conducted in the relatively low local field of the earth, the Bloch–Siegert effect can quickly become relevant. This is especially the case for SNMR experiments in the unsaturated zone, where due to short relaxation times fast pulses of high intensity must be used. To describe the Bloch–Siegert effect, we use the average Hamiltonian approximation obtained by the Magnus expansion of up to fifth order, as well as the solution of the Bloch equations. The results of these approximations are tested against the Bloch simulations and it is shown that they are only valid for limited ranges of the excitation field amplitude. The influence of the Bloch–Siegert effect on sensitivity kernels is described and verified with experimental data obtained with a small scale SNMR sensor on water containers.

Spin Currents Induced in Open-Shell Molecules by Static and Uniform Magnetic and Electric Fields in the Presence of a Spin-Orbit Coupling Interaction and Conservation Law.

The derivation of the total induced current density vector field, in the presence of static and uniform magnetic and electric fields, is illustrated in a more clear and formally correct language together with a discussion on the charge-current conservation law not presented before for the spin-orbit coupling contribution. The theory here exposed turns out to be in fully agreement with the theory of Special Relativity and it is applicable to open-shell molecules in the presence of a nonvanishing spin orbit coupling. The discussion here exposed turns out to be accurately valid for a strictly central field due to the chosen approximation of the spin-orbit coupling Hamiltonian, but it is appropriate to deal correctly with molecular systems. The ab initio calculation of spin current densities has been implemented at both unrestricted Hartree-Fock and unrestricted DFT levels of theory. Some maps of spin currents on molecules of interest, i.e., the CH3 radical and the superoctazethrene molecule are also illustrated.

Simple derivation of moiré-scale continuous models for twisted bilayer graphene

We provide a formal derivation of a reduced model for twisted bilayer graphene (TBG) from Density Functional Theory. Our derivation is based on a variational approximation of the TBG Kohn-Sham Hamiltonian and asymptotic limit techniques. In contrast with other approaches, it does not require the introduction of an intermediate tight-binding model. The so-obtained model is similar to that of the Bistritzer-MacDonald (BM) model but contains additional terms. Its parameters can be easily computed from Kohn-Sham calculations on single-layer graphene and untwisted bilayer graphene with different stackings. It allows one in particular to estimate the parameters $w_{\rm AA}$ and $w_{\rm AB}$ of the BM model from first-principles. The resulting numerical values, namely $w_{\rm AA}= w_{\rm AB} \simeq 126$ meV for the experimental interlayer mean distance are in good agreement with the empirical values $w_{\rm AA}= w_{\rm AB}=110$ meV obtained by fitting to experimental data. We also show that if the BM parameters are set to $w_{\rm AA}= w_{\rm AB} \simeq 126$ meV, the BM model is an accurate approximation of our reduced model.

Hartree–Fock analogue theory of thermo-optic interaction

Thermo-optic interaction significantly differs from the usual particle-particle interactions in physics, as it is retarded in time. A prominent platform for realising this kind of interaction are photon Bose–Einstein condensates, which are created in dye-filled microcavities. The dye solution continually absorbs and re-emits these photons, causing the photon gas to thermalize and to form a Bose–Einstein condensate. Because of a non-ideal quantum efficiency, these cycles heat the dye solution, creating a medium that provides an effective thermo-optic photon–photon interaction. So far, only a mean-field description of this process exists. This paper goes beyond by working out a quantum mechanical description of the effective thermo-optic photon–photon interaction. To this end, the self-consistent modelling of the temperature diffusion builds the backbone of the modelling. Furthermore, the manyfold experimental timescales allow for deriving an approximate Hamiltonian. The resulting quantum theory is applied in the perturbative regime to both a harmonic and a box potential for investigating its prospect for precise measurements of the effective photon–photon interaction strength.

Surface hopping simulations on charge separation in an organic donor-acceptor system.

Charge separation in organic solar cells is a long-lasting and heavily debated issue. Here, we use the surface hopping method based on the Pariser-Parr-Pople (PPP) Hamiltonian and configuration interaction singles (CIS) approximation to simulate the charge separation process in an organic donor-acceptor system. The system is composed of one donor polymer chain and four acceptor polymer chains, and they are all stacked face-to-face. We let the system to relax from a photoexcited state, and then we observed that the electron is transferred from the donor chain to different acceptor chains and the hole is left on the donor chain, forming polaron pairs with different electron-hole distances. By performing statistical analysis on a number of trajectories, we found that the electron and the hole are fully separated before the system relaxes to its lowest excited state. The yield of free charges shows a significant dependence on the donor-acceptor band offset which provides the driving force for charge separation, while showing negligible dependence on the photoexcitation energy. The external electric field has a remarkable effect on the yield of free charges.

A non-perturbative no-go theorem for photon condensation in approximate models

Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Recent no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be {\it spatially uniform}. However, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. %{It has also been recently shown that truncation of the Hilbert space of the matter system can affect the gauge invariance of the theory. However, it is always possible to obtain approximate Hamiltonians obeying the gauge principle in the truncated Hilbert space.} Here, we demonstrate a general no-go theorem valid also for truncated, gauge-invariant models which forbid first-order as well as second-order superradiant phase transitions in the absence of a coupling with a magnetic field. In particular, we explicitly consider the cases of interacting electrons in a lattice and $M$-level systems.

Many-body excitations in trapped Bose gas: A non-Hermitian approach

We study a physically motivated model for a trapped dilute gas of Bosons with repulsive pairwise atomic interactions at zero temperature. Our goal is to describe aspects of the excited many-body quantum states of this system by accounting for the scattering of atoms in pairs from the macroscopic state. We start with an approximate many-body Hamiltonian, H a p p \mathcal {H}_{\mathrm {app}} , in the Bosonic Fock space. This H a p p \mathcal {H}_{\mathrm {app}} conserves the total number of atoms. Inspired by Wu [J. Math. Phys. 2 (1961), 105–123], we apply a non-unitary transformation to H a p p \mathcal {H}_{\mathrm {app}} . Key in this procedure is the pair-excitation kernel, which obeys a nonlinear integro-partial differential equation. In the stationary case, we develop an existence theory for solutions to this equation by a variational principle. We connect this theory to a system of partial differential equations for one-particle excitation (“quasiparticle”-) wave functions derived by Fetter [Ann. Phys. 70 (1972), 67–101], and prove existence of solutions for this system. These wave functions solve an eigenvalue problem for a J J -self-adjoint operator. From the non-Hermitian Hamiltonian, we derive a one-particle nonlocal equation for low-lying excitations, describe its solutions, and recover Fetter’s energy spectrum. We also analytically provide an explicit construction of the excited eigenstates of the reduced Hamiltonian in the N N -particle sector of Fock space.

THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Tm ATOM WITHIN OPTIMIZED RELATIVISTIC MANY-BODY THEORY

Theoretical studying Rydberg spectrum of complex lanthanide atom of Tm has been performed within the relativistic many-body perturbation theory and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham-Breit ones. Optimization has been fulfilled by means of introduction of the special gauge parameter to the Fock and Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital sets, generated by the corresponding zeroth approximation Hamiltonian. The calculated energies and widths of autoionization resonant states 4f--1j 6s(J12)nsnp[J] of the Tm atom with n=25-35 are presented and compared with known theoretical results, received within other approaches. Two main types of the Rydberg autoionization resonances decay, namely, the classic Beutler-Fano decay channel and a new Ivanov et al reorientation-type decay channel ar4e studied. It is noted that, for example, for autoionization resonant states with the considered values of n, the decay of resonances occurs along both channels, and it is extremely difficult to understand a priori which of them is dominant.

Analytical results for phase bunching in the pendulum model of wave-particle interactions

Radiation belt electrons are strongly affected by resonant interactions with cyclotron-resonant waves. In the case of a particle passing through resonance with a single, coherent wave, a Hamiltonian formulation is advantageous. With certain approximations, the Hamiltonian has the same form as that for a plane pendulum, leading to estimates of the change at resonance of the first adiabatic invariant I, energy, and pitch angle. In the case of large wave amplitude (relative to the spatial variation of the background magnetic field), the resonant change in I and its conjugate phase angle ξ are not diffusive but determined by nonlinear dynamics. A general analytical treatment of slow separatrix crossing has long been available and can be used to give the changes in I associated with “phase bunching,” including the detailed dependence on ξ, in the nonlinear regime. Here we review this treatment, evaluate it numerically, and relate it to previous analytical results for nonlinear wave-particle interactions. “Positive phase bunching” can occur for some particles even in the pendulum Hamiltonian approximation, though the fraction of such particles may be exponentially small.

First-Principles Study of the RKKY Interaction and the Quadrupole Order in the Pr 1-2-20 Systems PrT2Al20 (T = Ti, V)

Electronic states and quadrupole orders in the Pr 1-2-20 systems PrT2Al20 (T=Ti, V) are investigated on the basis of the first-principles calculations. The effective 196 orbital model is derived to reproduce the first-principles electronic structures of LaT2Al20 (T=Ti, V) without contribution from the Pr 4f electrons which are considered to be well localized and is employed to calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between quadrupole and octupole moments of the Pr ions. Within the random phase approximation for the RKKY Hamiltonian, the most divergent susceptibility is found to be the quadrupole one for the wave vector Q = (0,0,0) in the case of PrTi2Al20 while that for Q = (pi/a,0,pi/a) in the case of PrV2Al20 as consistent with experimental observations in the both cases which exhibit the ferro-quadrupole (FQ) and the antiferro-quadrupole (AFQ) orders, respectively. We also discuss the ordered states using the mean-field approximation and find that, in the case of PrTi2Al20, the 1st-order phase transition to the O20 FQ order with a tiny discontinuity takes place as predicted by the Landau theory. In the case of PrV2Al20, the system exhibits two distinct O22 AFQ orders, AFQ-I and AFQ-II, and shows subsequent two phase transitions, the 2nd-order one from normal to AFQ-I and the 1st-order one from AFQ-I to AFQ-II, that may be responsible for the double transitions observed by specific heat measurements.

Theoretical analysis of the long-distance limit of NMR chemical shieldings.

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid-Based Quantum Simulations.

We have recently shown how program synthesis (PS), or the concept of “self-writing code”, can generate novel algorithms that solve the vibrational Schrödinger equation, providing approximations to the allowed wave functions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wave function ψ(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this Article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wave functions and energy eigenvalues of representative model PESs (both 1-D and multidimensional). We show that PS can generate algorithms that offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods that exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multidimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order of magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wave function propagation and evaluation of molecular electronic structure.

A Poisson map from kinetic theory to hydrodynamics with non-constant entropy

Kinetic theory describes a dilute monatomic gas using a distribution function f(q,p,t), the expected phase-space density of particles at a given position q with a given momentum p. The distribution function evolves according to the collisionless Boltzmann equation in the high Knudsen number limit. Fluid dynamics provides an alternative description of the gas using macroscopic hydrodynamic variables that are functions of position and time only. The mass, momentum and entropy densities of the gas evolve according to the compressible Euler equations in the limit of vanishing viscosity and thermal diffusivity. Both systems can be formulated as noncanonical Hamiltonian systems. Each configuration space is an infinite-dimensional Poisson manifold, and the dynamics is the flow generated by a Hamiltonian functional via a Poisson bracket. We construct a map J1 from the space of distribution functions to the space of hydrodynamic variables that respects the Poisson brackets on the two spaces. This map is therefore a Poisson map. It maps the p-integral of the Boltzmann entropy flogf to the hydrodynamic entropy density. This map belongs to a family of Poisson maps to spaces that include generalised entropy densities as additional hydrodynamic variables. The whole family can be generated from the Taylor expansion of a further Poisson map that depends on a formal parameter. If the kinetic-theory Hamiltonian factors through the Poisson map J1, an exact reduction of kinetic theory to fluid dynamics is possible. However, this is not the case. Nonetheless, by ignoring the contribution to the Hamiltonian from the entropy of the distribution function relative to its local Maxwellian, a distribution function defined by the p-moments ∫dnp(1,p,|p|2)f, we construct an approximate Hamiltonian that factors through the map. The resulting reduced Hamiltonian, which depends on the hydrodynamic variables only, generates the compressible Euler equations. We can thus derive the compressible Euler equations as a Hamiltonian approximation to kinetic theory. We also give an analogous Hamiltonian derivation of the compressible Euler–Poisson equations with non-constant entropy, starting from the Vlasov–Poisson equation.

Adiabatic projection: Bridging ab initio, density functional, semiempirical, and embedding approximations.

Modern electronic structure approximations routinely employ reference systems described by approximate Hamiltonians. This work introduces the adiabatic projection formalism for building formally exact corrections to such reference systems. Starting from the real Hamiltonian of a many-electron system, one constructs a reference system Hamiltonian by projecting the kinetic and electron-electron interaction operators onto "interesting" states. The reference system is corrected by density functionals for the difference between the projected and unprojected kinetic and electron-electron energies. These density functionals are constructed from adiabatic connections between the reference and real systems. The Hohenberg-Kohn theorems imply the existence of exact functionals, which can ensure that the reference system's ground-state energy and density match the real system. Adiabatic projection further generalizes Kohn-Sham density functional theory (DFT) and the generalized adiabatic connection [W. Yang, J. Chem. Phys. 109, 10107 (1998)] and recovers these methods for certain choices of projection operators. Other choices of projection operators offer new opportunities, including formally exact and systematically improvable analogues to wavefunction-in-DFT embedding, DFT+U, and semiempirical theories. Numerical results are presented for two representative choices: a projected exchange-correlation correction to small-basis-set coupled cluster theory and a projected kinetic energy density functional correcting basis set errors in DFT. The latter offers performance for dimerization energies approaching the Boys-Bernardi counterpoise correction while also correcting intramolecular basis set superposition errors.

Probing protein aggregation at buried interfaces: distinguishing between adsorbed protein monomers, dimers, and a monomer-dimer mixture in situ.

Protein adsorption on surfaces greatly impacts many applications such as biomedical materials, anti-biofouling coatings, bio-separation membranes, biosensors, antibody protein drugs etc. For example, protein drug adsorption on the widely used lubricant silicone oil surface may induce protein aggregation and thus affect the protein drug efficacy. It is therefore important to investigate the molecular behavior of proteins at the silicone oil/solution interface. Such an interfacial study is challenging because the targeted interface is buried. By using sum frequency generation vibrational spectroscopy (SFG) with Hamiltonian local mode approximation method analysis, we studied protein adsorption at the silicone oil/protein solution interface in situ in real time, using bovine serum albumin (BSA) as a model. The results showed that the interface was mainly covered by BSA dimers. The deduced BSA dimer orientation on the silicone oil surface from the SFG study can be explained by the surface distribution of certain amino acids. To confirm the BSA dimer adsorption, we treated adsorbed BSA dimer molecules with dithiothreitol (DTT) to dissociate these dimers. SFG studies on adsorbed BSA after the DTT treatment indicated that the silicone oil surface is covered by BSA dimers and BSA monomers in an approximate 6 : 4 ratio. That is to say, about 25% of the adsorbed BSA dimers were converted to monomers after the DTT treatment. Extensive research has been reported in the literature to determine adsorbed protein dimer formation using ex situ experiments, e.g., by washing off the adsorbed proteins from the surface then analyzing the washed-off proteins, which may induce substantial errors in the washing process. Dimerization is a crucial initial step for protein aggregation. This research developed a new methodology to investigate protein aggregation at a solid/liquid (or liquid/liquid) interface in situ in real time using BSA dimer as an example, which will greatly impact many research fields and applications involving interfacial biological molecules.