Wigner function and the entanglement of quantized Bessel—Gaussian vortex state of quantized radiation field

A new kind of quantum non-Gaussian state with vortex structure, termed Bessel-Gaussian vortex state, is constructed, which is an eigenstate of sum of squared annihilation operators a² + b². The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality. It is also found that quantized vortex state is always in entanglement. And a scheme for generating such quantized vortex states is proposed.     

Non-Gaussianity of photon-added-then-subtracted squeezed vacuum state

In this paper, the photon-added-then-subtracted squeezed vacuum state (PASSVS), a non-Gaussian state, is presented by adding then subtracting photon to a squeezed vacuum state. It is found that PASSVS is just a superposition state between S(r) | 0〉 and S(r) | 2〉, where S(r) is the single-mode squeezing operator with the squeezing parameter r. Its non-Gaussianity is exhibited via its Wigner function and the Hilbert–Schmidt distance. In addition, a possible scheme is presented to produce the PASSVS by virtue of the cavity QED.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Enhancing entanglement of entangled coherent states by single-mode coherent superposition of photon subtraction and addition

We introduce a new entangled quantum state generated by applying single-mode coherent superposition of photon subtraction and addition (a^† cos θ + a sin θ)^m to the entangled coherent state |Ψ_±(α,0)〉$|{\Psi }_{\pm }\left(\alpha ,0\right)〉$, and then investigate the entanglement properties affected by coherent superposition operation. It is shown that this operation can be applied to enhance the entanglement of the state |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$. In addition, the effects of the coherent operation is better to improve the entanglement than that of the creation operation (a^†m) for |Ψ₊(α,0)〉$|{\Psi }_{+}\left(\alpha ,0\right)〉$ in a small-amplitude regime and for |Ψ₋(α,0)〉$|{\Psi }_{-}\left(\alpha ,0\right)〉$ in any regime.     

光子增减叠加相干态在热环境中的退相干

研究了由光子增减叠加操作作用于相干态而得量子态的非经典性及其在热环境中的退相干问题.通过解析导出了Mandel's Q参数、光子数分布、Wigner函数等,讨论其非经典性.研究表明一阶光子增减相干叠加相干态在相空间总是取负值,只要满足条件∣2z* +α-α*∣2＜1.基于Wigner函数的演化积分公式,解析地推导出了在热环境中Wigner函数的简洁表达式.研究首次表明:如果κt＜1/2ln[(2(η)+2)/(2(η)+1)]得以满足,一阶光子增减相干叠加相干态在相空间最小值点处Wigner函数分布总存在负部.此外,根据Wigner函数负部体积讨论了其非经典特性.     

Nonclassicality and Decoherence of Photon-Subtraction Squeezing-Enhanced Thermal State

We introduce a kind of non-Gaussian state—photon-subtracted squeezing-enhanced thermal state (PSSETS) characteristics by two-squeezing parameters (λ,r). Its normalization factor is a Legendre polynomial of two-squeezing parameters and average photon number of the thermal state. The nonclassicality is investigated by using the negativity of Wigner function (WF). It is shown that the single PSSETS always has negative values when . The decoherence effect on PSSETS is then included by analytically deriving the time evolution of WF. For the single PSSETS, the characteristic time is longer than that of photon-subtracted squeezing thermal state.     

Non-classical properties of superposition of two coherent states having phase difference ?

Recently Ahmad et al. [Optik 2009;120;68; Optics Commun. 2007;271:162; Chin. Phys. Lett. 2006;23:2438] have studied non-classical properties of superposition of two-coherent states of the form, |ψ〉=K[|α〉+eiξ|αei?〉] for the special cases with values ? = π/2,  3π/2,  and π, and for arbitrarily fixed values of ξ. We point out that some of their results are special cases of our recently published work [Physica A 319, 305 (2003); Physica A 341, 201(2004)] on the most general superposition of two arbitrary coherent states of the form ∼(Z₁|α〉+Z₂|β〉), where X_1,2, α and β are arbitrary and only restriction on these is the normalization condition for the superposed state. To make our point we first obtain results for (i) squeezing of the most general Hermitian operator X_θ = X₁ cos θ + X₂ sin θ, with X₁ + iX₂ = a, is the annihilation operator, and (ii) sub-Poissonian photon statistics, for the superposed state |ψ〉 with a general ? and, then obtain results of Ahmad et al. for ? = π/2,  3π/2,  and π and for θ = 0 and π/2. It is interesting to note that the arbitrarily fixed values ξ = |α|² and −|α|² for ? = π/2 and 3π/2, respectively by Ahmad et al. are the values at which we get maximum squeezing working in a rigorous way.     

Large amplitude bending motion in CsOH, studied through ab initio-based three-dimensional potential energy functions

The large-amplitude bending motion in CsOH, a ‘classical’ molecule whose microwave spectrum was first recorded in 1967, has been studied ab initio. The three-dimensional potential energy surface has been calculated at the RCCSD(T)_DK3/[QZP + g ANO-RCC (Cs, O, H)] level of theory and employed in MORBID calculations of the rotation-vibration energies and intensities. The ground electronic state is ¹Σ⁺ with the equilibrium structure r_e(Cs-O) = 2.3930 Å, r_e(O-H) = 0.9587 Å, and ∠_e(Cs-O-H) = 180.0°. The O-H moiety is bound to Cs by an ionic bond and the molecule can be described as Cs^δ+(OH)^δ-. Hence, the bending potential is shallow and gives rise to large-amplitude bending motion. The ro-vibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are 〈r(Cs-O)〉₀ = 2.3987 Å, 〈r(O-H)〉₀ = 0.9754 Å, and 〈∠(Cs-O-H)〉₀ = 163°. Although the averaged structure in the vibrational ground state is far from being linear, the Yamada-Winnewissi-linearity parameter for CsOH is γ₀≈-1.0, the value characteristic for a linear molecule.     

FT-FIR-spectrum and the ground state constants of D2CO

The ground state spectrum of the formaldehyde D₂¹³CO molecule in the range from 25 to 360 cm⁻¹ has been recorded by a Fourier transform infrared spectrometer. The quantum number limits of the assigned transitions are J = 6-54 and K_a = 0-16. The data was fitted into Watson’s A- and S-reduced Hamiltonians in I^r-representation up to eighth order. The determinable constants calculated from both reductions are compared. The standard deviation of the far infrared data is 3.0 MHz. The spectroscopic constants are also calculated to high accuracy at the CCSD(T)/cc-pVQZ level of ab initio theory and agree well with the experimental ones.     

Superpositions of excited–deexcited coherent states and some of their non-classical properties

Applying the operator a + a⁺ to the superposed coherent states several times, superpositions of the excited–deexcited coherent states are obtained. Compared with the original superposed coherent states, these new states can have stronger squeezing and anti-bunching effects. The operation a + a⁺ can also induce squeezing or antibunching effect if the original states do not possess these properties. Calculations about the phase properties, the Q function and the Wigner function reflect the non-classical character of the excited–deexcited states from different aspects.     

The Squeezing Effect of Three-Mode Operator as an Extension from Two-Mode Squeezing Operator

We theoretically study the squeezing effect in a 3-wave mixing process, generated by the operator S₃ o exp[m(a₁a₂-a₁^fa₂^f)+n(a₁a₃-a₁^fa₃^f)]S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]. The corresponding 3-mode squeezed vacuum state in Fock space and its uncertainty relation are presented. It turns out that S ₃ may exhibit enhanced squeezing. By virtue of integration within an ordered product (IWOP) of operators, we also give the S ₃’s normally ordered expansion. Finally, we calculate the Wigner function of 3-mode squeezed vacuum state by using the Weyl ordering invariance under similar transformations.     

Rotational spectra of isotopic species of SO2F2: experimental and ab initio structures

The rotational spectra of ³⁴SO₂F₂ and S¹⁸O¹⁶OF₂ have been measured in their ground vibrational state between 9 and 110 GHz. Accurate rotational constants have been derived. Various experimental structures including the average structure have been determined. The ab initio structure has been calculated at the CCSD(T) level of theory. The different structures are compared and the best equilibrium structure is the ab initio structure: r_e(SO)=1.401 (3) Å, r_e(SF)=1.532 (3) Å, ∠_e(OSO)=124.91(20)°, ∠_e(FSF)=95.53 (20)°.     

Rovibrational spectrum and potential energy surface of the N2-N2O van der Waals complex

The rovibrational spectrum of the N₂-N₂O van der Waals complex has been recorded in the N₂O ν₁ region (∼1285 cm⁻¹) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observed transitions together with the data observed previously in the N₂O ν₃ region are analyzed using a Watson S-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for the ground and excited vibrational states are accurately determined. The band-origin of the spectrum is determined to be 1285.73964(14) cm⁻¹. A restricted two-dimensional intermolecular potential energy surface for a planar structure of N₂-N₂O has been calculated at the CCSD(T) level of theory with the aug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at the ground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm⁻¹ at θ_N2 = 11.0° and θ_N2O = 84.3° and has a saddle point with a barrier height of 204.61 cm⁻¹ at θ_N2 = 97.4° and θ_N2O = 92.2°, where θ_N2(θ_N2O) is the enclosed angle between the N-N axis (N-N-O axis) and the intermolecular axis.     

Enhancement of Non-Gaussianity and Nonclassicality of Photon-Added Displaced Fock State: A Quantitative Approach

Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures, namely entanglement potential, Wigner–Yanese skew information, Wigner logarithmic negativity, and relative entropy of non-Gaussianity. It is observed that Fock parameter always increases the amount of nonclassicality and non-Gaussianity, while photon addition is effective only for small values of the displacement parameter. Further, the nonclassical and non-Gaussian effects decrease initially with an increase in the displacement parameter before increasing for the large displacement to saturate to the corresponding Fock state (equivalently displaced Fock state) value. Finally, dynamics of the Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.     

Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

A new kind of quantum non-Gaussian state with a vortex structure,termed a Bessel-Gaussian vortex state,is constructed,which is an eigenstate of the sum of squared annihilation operators a2+b2.The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality.It is also found that a quantized vortex state is always in entanglement.And a scheme for generating such quantized vortex states is proposed.     

A theoretical study of BrCN in the Π electronic ground state: Large amplitude bending motion

We have calculated the three-dimensional potential energy surfaces for the 1 ²A′ and 1 ²A″ states of BrCN⁺ at the MR-SDCI_DK+Q/[QZP-ANO-RCC (Br, C, N)] level of theory, where MR-SDCI_DK means ‘multi-reference single and double excitation configuration interaction calculation with Douglas-Kroll Hamiltonian.’ These ab initio potential energy surfaces have a common minimum (corresponding to the state) at a linear equilibrium structure with r_e(Br-C) = 1.735 Å and r_e(C-N) = 1.199 Å. Variational RENNER calculations yield a zero-point averaged structure (with the structural parameters calculated as expectation values over rovibrational wavefunctions) with 〈r(Br-C)〉₀ = 1.739 Å, 〈r(C-N)〉₀ = 1.204 Å, and 〈∠(Br-C-N)〉₀ = 172(4)°. A severe Fermi resonance between 2ν₂ and ν₃ has been found theoretically for the ²A″ potential energy surface. Comparing the ab initio zero-point averaged structure with a recent, experimentally derived r₀ structure, it is concluded that the effects of large-amplitude bending motion should be taken into account explicitly in the process of deriving the r₀ structure from the experimental values of the rotational constants. The electronic structure of BrCN⁺ has also been discussed.     

A theoretical study of FeCN in the Δ electronic ground state

The three-dimensional potential energy and dipole moment surfaces for the electronic ground state ⁶Δ of FeCN have been computed at the MR-SDCI + Q + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, where MR-SDCI means ‘multi-reference single and double excitation configuration interaction’ and ANO means ‘atomic natural orbital’. Based on these potential energy and dipole moment surfaces, the spectroscopic parameters, rovibronic energies, structural parameters, vibrational transition moments, and the wavenumbers and intensities of selected rotation-vibration transitions have been calculated. The equilibrium structure is linear with r_e(Fe-C) = 2.048 Å and r_e(C-N) = 1.168 Å, and the zero-point averaged structure is bent with 〈r(Fe-C)〉₀ = 2.082 Å, 〈r(C-N)〉₀ = 1.172 Å, and 〈∠(Fe-C-N)〉₀ = 170(5)°. At all the MR-SDCI + Q and the size-extensive multi-reference averaged quadratic coupled-cluster (MR-AQCC) levels of theory, with and without relativistic correction E_rel, that were employed in the present work, ⁶Δ FeCN is predicted to be slightly more stable than ⁶Δ FeNC. For example, the energy difference between the two isomers is approximately 150 cm⁻¹ at the highest level of theory employed, MR-AQCC + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] with zero-point energy correction. The electronic structure of ⁶Δ FeCN has also been compared with that of ⁶Δ FeNC. At present, no experimental spectroscopic data are available for ⁶Δ FeCN. It is hoped that the present work will stimulate experimental investigations of this molecule.     

Microwave spectrum and structure of furfural

The microwave spectrum of furfural was investigated in the frequency range 7 GHz-21 GHz and 49 GHz-330 GHz. The ground and first torsional state of trans-furfural and ground state of cis-furfural were assigned and analyzed. A total of 1720 rotational lines with J up to 100 and K_a up to 53 were assigned to the ground state of trans-furfural, 1406 rotational lines with J up to 100 and K_a up to 48 were assigned to the first torsional state of trans-furfural and 2103 rotational lines with J up to 90 and K_a up to 48 to the ground state of cis-furfural. Accurate sets of centrifugal distortion constants for both conformations have been determined for the first time. The spectra of all ¹³C and ¹⁸O singly substituted isotopic species were observed in natural abundance in the 7 GHz-21 GHz range. Molecular structure co-ordinates, bond lengths and angles of the Kraitchman substitution type (r_s) and pseudo-Kraitchman type (r_pKr) are derived from the isotopic studies.     

Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K_c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although dimethylsulfoxide is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r) but the least-squares system of normal equations is better conditioned with representation I^r. These results are compared to those obtained for a few typical molecules.     

S0 and S1 spectroscopy of jet cooled 9-cyano-10-methylanthracene: The methyl group as a molecular rotor

Jet-cooled fluorescence excitation and dispersed fluorescence spectra of 9-methylanthracene (MA), 9-cyanoanthracene (CA) and 9-cyano-10-methylanthracene (CMA) have been measured. The spectra of MA and CMA near the S₀-S₁ origin reveal a prominent torsional progression due to the hindered methyl group rotation and its torsional vibration against the aromatic ring frame. Additionally, the laser induced fluorescence LIF excitation spectrum of CMA shows the splitting of many vibrational modes.Observed positions and relative intensities of the methyl internal rotational bands were interpreted in terms of transitions calculated based on the quantum mechanical one-dimensional rotor. The low-frequency vibrational bands were interpreted also with the all electron quantum mechanical calculations within the RHF/6-31G(d,p), CIS/3-21G and CIS/6-31G(d,p) approximations. It is predicted that in the case of MA the eclipsed geometry (one C-H in the plane of the ring) is most stable in both S₀ and S₁ states. Conformation of the methyl group in CMA is suggested to change upon S₁ ← S₀ excitation (π/12 phase shift of the methyl group). The predicted energy barrier for methyl group rotation in the S₀ state of CMA is considerably higher (72 cm⁻¹) than that in the S₁ state (22 cm⁻¹). Following the present quantum mechanical calculations, the carbon atom of the methyl group belongs to the aromatic plane in the S₀ ground state but it deviates from this plane in the S₁ excited state. These in turn suggest that the calculated barrier for methyl group rotation in CMA has a 6-fold symmetry in the S₀ ground state and roughly a 4-fold symmetry in the S₁ state.