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Register a new userLow-Energy Scattering Properties of Ground-State and Excited-State Positronium Collisions
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Low-energy elastic and inelastic scattering in the Ps(1$s$)-Ps(2$s$) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum $L=0$ and parity equal to $+1$. The s-wave scattering lengths for the asymptotic Ps(1$s$)-Ps(2$s$) channel are calculated for each spin configuration. Results obtained for the s-wave scattering lengths are $a_{mathrm{TT}}=$~$7.3(2)a_0-i0.02(1)a_0$, $a_{mathrm{SS}}=$~$13.2(2)a_0-i0.9(2)a_0$, and $a_{mathrm{ST}}=$~$9.7(2)a_0$ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross-sections are carried-out for Ps atoms initially prepared in different uncoupled spin states.
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We measure inelastic collisional cross sections for the ground $^3$F$_2$ state and the excited $^3$P$_0$ state of atomic thorium in cold collisions with $^3$He. We determine for Th ($^3$F$_2$) at 800 mK the ratio $gamma approx 500$ of the momentum-transfer to Zeeman relaxation cross sections for collisions with $^3$He. For Th ($^3$P$_0$), we study electronic inelastic processes and find no quenching even after $10^6$ collisions. We also determine the radiative lifetime of Th ($^3$P$_0$) to be $tau > 130$ ms. This great stability of the metastable state opens up the possibility for further study, including trapping.
Since their first experimental observation, ultralong-range Rydberg molecules consisting of a highly excited Rydberg atom and a ground state atom have attracted the interest in the field of ultracold chemistry. Especially the intriguing properties like size, polarizability and type of binding they inherit from the Rydberg atom are of interest. An open question in the field is the reduced lifetime of the molecules compared to the corresponding atomic Rydberg states. In this letter we present an experimental study on the lifetimes of the ^3Sigma (5s-35s) molecule in its vibrational ground state and in an excited state. We show that the lifetimes depends on the density of ground state atoms and that this can be described in the frame of a classical scattering between the molecules and ground state atoms. We also find that the excited molecular state has an even more reduced lifetime compared to the ground state which can be attributed to an inward penetration of the bound atomic pair due to imperfect quantum reflection that takes place in the special shape of the molecular potential.
We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground $S$ state Li atom, one excited $P$ state Li atom and one ground $S$ state Li$^+$ ion, Li($2,^{2}S$)-Li($2,^{2}P$)-Li$^+(1,^{1}S$). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive collective interactions (appearing in second-order) induced by the energy degeneracy and enhanced by the induction effect of the Li$^+$ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero leaving only three-body nonadditive collective interactions making the present system potentially a platform to explore quantum three-body collective effects. We also extract first-principles leading coefficients of the long-range electrostatic, induction, and dispersion energies of Li$^+_2$ electronic states correlating to Li($2,^{2}P$)-Li$^+(1,^{1}S$), which until now were not available in the literature. The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.
Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of a quantum many-body system. While QKSD algorithms have typically relied on using the Hadamard test for estimating Krylov subspace matrix elements of the form, $langle phi_i|e^{-ihat{H}tau}|phi_j rangle$, the associated quantum circuits require an ancilla qubit with controlled multi-qubit gates that can be quite costly for near-term quantum hardware. In this work, we show that a wide class of Hamiltonians relevant to condensed matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multi-fidelity estimation protocol that can be used to compute such quantities showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, we develop a unified theory of quantum Krylov subspace algorithms and present three new quantum-classical algorithms for the ground and excited-state energy estimation problem, where each new algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.
Quantum chemistry is one of the important applications of quantum information technology. Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential. In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them. Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing. The key idea is to combine a Ramsey type measurement with the quantum annealing. This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap. Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian. We show robustness against non-adiabatic transitions between the ground state and first-excited state. Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.
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