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Register a new userFour-Dimensional Scaling of Dipole Polarizability in Quantum Systems
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Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $alpha$, rely on different scaling laws $alpha propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of atom-like quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $alpha = C (4 mu q^2/hbar^2)L^4$, where $mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless ratio between effective excitation energies, and the characteristic length $L$ is defined via the $mathcal{L}^2$-norm of the position operator. The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules.
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Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability ($alpha_d$) of the Cd atom are not in good agreement with the available experimental value of $49.65(1.65) e a_0^3$. Among these two are finite-field approaches in which the relativistic effects have been included approximately, while the other calculation uses a four component perturbed RCC method. However, another work adopting an approach similar to the latter perturbed RCC method gives a result very close to that of experiment. The major difference between these two perturbed RCC approaches lies in their implementation. To resolve this ambiguity, we have developed and employed the relativistic normal coupled-cluster (RNCC) theory to evaluate the $alpha_d$ value of Cd. The distinct features of the RNCC method are that the expression for the expectation value in this approach terminates naturally and that it satisfies the Hellmann-Feynman theorem. In addition, we determine this quantity in the finite-field approach in the framework of A four-component relativistic coupled-cluster theory. Considering the results from both these approaches, we arrive at a reliable value of $alpha_d=46.02(50) e a_0^3$. We also demonstrate that the contribution from the triples excitations in this atom is significant.
The cesium 6S_1/2 scalar dipole polarizability alpha_0 has been determined from the time-of-flight of laser cooled and launched cesium atoms traveling through an electric field. We find alpha_0 = 6.611+-0.009 x 10^-39 C m^2/V= 59.42+-0.08 x 10^-24 cm^3 = 401.0+-0.6 a_0^3. The 0.14% uncertainty is a factor of fourteen improvement over the previous measurement. Values for the 6P_1/2 and 6P_3/2 lifetimes and the 6S_1/2 cesium-cesium dispersion coefficient C_6 are determined from alpha_0 using the procedure of Derevianko and Porsev [Phys. Rev. A 65, 053403 (2002)].
We present electric dipole polarizabilities ($alpha_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.
Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in exceeding conventional limitations. For that, we primarily need to contemplate the fundamental principles and concepts from a nonstationarity perspective. Here, we revisit one of those concepts: The polarizability of a small particle, assuming that its properties vary in time. We describe the coupling of the induced dipole moment with the excitation field in a nonstationary, causal way, and introduce a complex-valued function, called temporal complex polarizability, for elucidating a nonstationary Hertzian dipole under time-harmonic illumination. This approach can be extended to any subwavelength particle having electric response. In addition, we also study the polarizability of a classical electron through the equation of motion whose damping coefficient and natural frequency are changing in time. We theoretically derive the effective permittivity corresponding to time-varying media (comprising free or bound electrons) and explicitly show the differences with the conventional macroscopic Drude-Lorentz model. This paper will hopefully pave the road towards the understanding of nonstationary scattering from small particles and the homogenization of time-varying materials, metamaterials, and metasurfaces.
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.
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