Standard Two-level System Research Articles

Thermal emission from the amorphous dust: An alternative possibility of the origin of the anomalous microwave emission

Abstract Complete studies of the radiative processes of thermal emission from the amorphous dust from microwave through far-infrared wavebands are presented by taking into account, self-consistently for the first time, the standard two-level systems (TLS) model of amorphous materials. The observed spectral energy distributions (SEDs) for the Perseus molecular cloud (MC) and W 43 from microwave through far-infrared are fitted with the SEDs calculated with the TLS model of amorphous silicate. We have found that the model SEDs reproduce the observed properties of the anomalous microwave emission (AME) well. The present result suggests an alternative interpretation for the AME being carried by the resonance emission of the TLS of amorphous materials without introducing new species. Simultaneous fitting of the intensity and polarization SEDs for the Perseus MC and W 43 are also performed. The amorphous model reproduces the overall observed feature of the intensity and polarization SEDs of the Perseus MC and W 43. However, the model’s predicted polarization fraction of the AME is slightly higher than the QUIJOTE upper limits in several frequency bands. A possible improvement of our model to resolve this problem is proposed. Our model predicts that interstellar dust is amorphous materials with very different physical characteristics compared with terrestrial amorphous materials.

Limitations of rotating-wave approximation in magnetic resonance: characterization and elimination of the Bloch–Siegert shift in magneto-optics

We present investigations of radio-frequency (RF) resonances observed in an optically pumped rubidium vapor. By measuring the systematic shifts (the Bloch–Siegert shifts) of RF resonances in low magnetic fields, we demonstrate limitations of the rotating-wave approximation in the case of angular momentum F ≥ 1. The resonance shifts and deformations are characterized in a wide range of parameters and it is shown that the observed behavior is far more complex than in a standard two-level system. It is also demonstrated that the shifts can be controllably turned on or off by switching between the oscillating and rotating magnetic field. Experimental results are supported with numerical calculations, reproducing all features of the observed signals. Besides fundamental aspect of the research, application of rotating magnetic field helps to suppress/evaluate spectroscopic-measurement and precise-metrology systematic errors. The reported study has also important implications for quantum metrology and information processing beyond RWA and standard two-state qubit dynamics.

Dynamical Evolution of an Effective Two-Level System with Symmetry**Supported by the National Natural Science Foundation of China under Grant Nos 11104171, 11404199, 11574187 and 11604188, the Youth Science Foundation of Shanxi Province of China under Grant No 2012021003-1, and the Natural Science Foundation for Youths of Shanxi Province under Grant Nos 201601D201027 and 1331KSC.

We investigate the dynamics of parity- and time-reversal symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the z components of the fixed points is the feature of the symmetry breaking and the projections in the x–y plane can be controlled with high flexibility compared with the standard two-level system with the symmetry. It helps to study the dynamic behavior of the complex symmetric model.

Realistic tunnelling states for the magnetic effects in non-metallic real glasses

The discovery of magnetic and compositional effects in the low-temperature properties of multi-component glasses has prompted the need to extend the standard two-level systems (2LSs) tunnelling model. A possible extension assumes that a subset of tunnelling quasi-particles is moving in a three-welled potential (TWP) associated with the ubiquitous inhomogeneities of the disordered atomic structure of the glass. We show that within an alternative, cellular description of the intermediate-range atomic structure of glasses the tunnelling TWP can be fully justified. We then review how the experimentally discovered magnetic effects can be explained within the approach where only localized atomistic tunnelling 2LSs and quasi-particles tunnelling in TWPs are allowed. We discuss the origin of the magnetic effects in the heat capacity, dielectric constant (real and imaginary parts), polarization echo and SQUID magnetization in several glassy systems. We conclude by commenting on a strategy to reveal the mentioned tunnelling states (2LSs and TWPs) by means of atomistic computer simulations and discuss the microscopic nature of the tunnelling states in the context of the potential energy landscape of glass-forming systems

Photoinduced Electron Transfer and Persistent Spectral Hole-Burning in Natural Emerald

Wavelength-selective excited-state lifetime measurements and absorption, luminescence, and hole-burning spectra of a natural African emerald crystal are reported. The (2)E excited-state lifetime displays an extreme wavelength dependence, varying from 190 to 37 μs within 1.8 nm of the R(1)-line. Overall, the excited state is strongly quenched, in comparison to laboratory-created emerald (τ=1.3 ms), with an average quenching rate of ∼6 × 10(3) s(-1) at 2.5 K. This quenching is attributed to photoinduced electron transfer caused by a relatively high concentration of Fe(2+) ions. The forward electron-transfer rate, k(f), from the nearest possible Fe(2+) sites at around 5 Å is estimated to be ∼20 × 10(3) s(-1) at 2.5 K. The photoreductive quenching of the excited Cr(3+) ions by Fe(2+) is followed by rapid electron back-transfer in the ground state upon deactivation. The exchange interaction based quenching can be modeled by assuming a random quencher distribution within the possible Fe(2+) sites with the forward electron-transfer rate, k(f), given as a function of acceptor-donor separation R by exp[(R(f)-R)/a(f)]; R(f) and a(f) values of 13.5 and 2.7 Å are obtained at 2.5 K. The electron transfer/back-transfer reorganizes the local crystal lattice, occasionally leading to a minor variation of the short-range structure around the Cr(3+) ions. This provides a mechanism for spectral hole-burning for which a moderately high quantum efficiency of about ∼0.005% is observed. Spectral holes are subject to spontaneous hole-filling and spectral diffusion, and both effects can be quantified within the standard two-level systems for non-photochemical hole-burning. Importantly, the absorbance increases on both sides of broad spectral holes, and isosbestic points are observed, in accord with the expected distribution of the "photoproduct" in a non-photochemical hole-burning process.

Variational properties of a pumped dynamical system

We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial state of the system. In this paper, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated, and the behaviour obtained is illustrated by numerical treatment of the standard two-level system with pumping and relaxation included.

Multiple-well tunneling model for the magnetic-field effect in ultracold glasses

Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low temperatures $T$ to static magnetic fields $B$ have been reported in the last decade and call for an extension of the standard two-level systems tunneling model. An explanation is proposed, capable of capturing at the same time the $T$- and $B$-dependence of the specific heat $C_p$ and of the dielectric constant $\epsilon$ in these glasses. This theory points to the existence of anomalous multi-welled tunneling systems in the glasses -- alongside the standard two-level systems -- and indications are given for glasses which should achieve larger electric magnetocapacitive enhancements.

Temperature dependence of the frequency and noise of superconducting coplanar waveguide resonators

We present measurements of the temperature and power dependence of the resonance frequency and frequency noise of superconducting niobium thin-film coplanar waveguide resonators carried out at temperatures well below the superconducting transition (Tc=9.2K). The noise decreases by nearly two orders of magnitude as the temperature is increased from 120to1200mK, while the variation of the resonance frequency with temperature over this range agrees well with the standard two-level system (TLS) model for amorphous dielectrics. These results support the hypothesis that TLSs are responsible for the noise in superconducting microresonators and have important implications for resonator applications such as qubits and photon detectors.

Do Proteins at Low Temperature Behave as Glasses? A Single-Molecule Study

We have recorded long spectral diffusion trajectories from individual LH2 pigment-protein complexes from the purple bacterium Rhodobacter sphaeroides at 1.4 K. From these data, the spectral cumulants of the absorption lines of individual, protein-embedded BChl a pigments have been evaluated. It appears that the first and second cumulants cannot be described by the predictions of the well tested standard two-level system (TLS) model for spectral diffusion in glasses. The results of the present study clearly show that there is a fundamental difference between the relaxation behavior of our test protein and that of glasses.

Vibronic Excitation of Single Molecules: A New Technique for Studing Low‐Temperature Dynamics

Herein, we present vibronic excitation and detection of purely electronic zero-phonon lines (ZPL) of single molecules as a new tool for investigating dynamics at cryogenic temperatures. Applications of this technique to study crystalline and amorphous matrix materials are presented. In the crystalline environment, spectrally stable ZPLs are observed at moderate excitation powers. By contrast, investigations at higher excitation intensities reveal the opening of local degrees of freedom and spectral jumps, which we interpret as the observation of elementary steps in the melting of a crystal. We compare these results to spectral single-molecule trajectories recorded in a polymer. The way in which much more complicated spectral features can be analysed is shown. Surprisingly, pronounced spectral shifts on a previously not accessible large energy scale are observed, which are hard to reconcile with the standard two-level model system used to describe low-temperature dynamics in disordered systems.

Theory of the thermal magnetocapacitance of multicomponent silicate glasses at low temperature

An explanation is put forward for the early findings of Zeller and Pohl (1971, Phys. Rev. B, 4, 2029) and, in particular, Stephens (1976, Phys. Rev. B, 13, 852), and then for the more comprehensive recent findings of Meißner and Strehlow (2000) for the anomalous magnetic-field-dependent behaviour of the heat capacity of some multicomponent glasses at low temperature (0.1 < T < 4 K) and in weak-to-moderate fields (0 < B < 8T). An essential new ingredient of this theory, together with the standard two-level system approach for cold glasses, is a multi-minima local potential for the quantum motion of metallic ions between near-degenerate wells, separated by relatively shallow barriers. Taking the tunneling entities as independent and assuming a novel probability distribution for the parameters of the multi-welled potential, an expression for the heat capacity C(T,B) is obtained with features that match rather well the reported unusual experimental data for the glasses. The indication coming from this theory for the data available is that the entities involved in tunnelling are nanoclusters of coherent ions.

Dynamics of amorphous polymers in the temperature region 2– [formula omitted] where the standard model of low-temperature glasses begin to fail: studies by single molecule spectroscopy and comparison with photon echo data

Spectra of single tetra-tert-butylterrylene molecules incorporated in purely amorphous polyisobutylene matrix have been measured at 2, 4.5 and 7 K (244, 381 and 187 molecules, correspondingly). This is a temperature region, where the main assumptions of the standard two-level system (TLS) model of low-temperature glasses begin to be not valid. At T=2 K the main parameters of most of the registered spectra were found to be consistent with the standard TLS model. At T=4.5 and 7 K some deviations from predictions of this model were observed. The detailed analysis reveals that increasing of temperature leads to additional, in comparison with the predictions of the standard TLS model, line broadening of spectral peaks. This additional line broadening was attributed to the influence of quasi-local low-frequency modes (LFMs) of the amorphous matrix in system under study at T=4.5 and 7 K . Distributions of single spectral peak widths of the detected spectra (the line width distributions) have been calculated and compared with the line width distributions simulated for the same system. Comparative analysis of experimental and simulated distributions allows to evaluate the value of LFM contribution at 4.5 and 7 K . The single molecule spectroscopy data were compared with the literature values of inverse optical dephasing times, 1/ πT 2, as measured for the same system by photon echo (S.J. Zilker et al., J. Chem. Phys. 109 (1998) 6780).

Dynamics of a doped polymer at temperatures where the two-level system model of glasses fails: Study by single-molecule spectroscopy

We investigated the spectra of a large number of single tetra-tert-butylterrylene molecules embedded in an amorphous polyisobutylene matrix and analyzed the distributions of their linewidths (widths of single spectral peaks). The measurements were performed at 2, 4.5, and 7 K. This is a temperature region, where the standard two-level system (TLS) model of low-temperature glasses begins to fail. At T=2 K the temporal behavior (history of frequency jumps) of most of the measured spectra and their linewidth distributions were found to be consistent with the TLS model. At higher temperatures the main features of individual spectra (number of spectral peaks, temperature variation of peak widths, ratio of intensities of different peaks, etc.) still appear consistent with the predictions of this model. An increase of temperature leads mainly to the broadening of spectral peaks. A detailed analysis of the linewidth distributions reveals deviations from a standard TLS model at T=4.5 and 7 K. This difference is attributed to the influence of quasi-local low-frequency modes (LFM) of the amorphous matrix. By comparing the measured linewidth distributions with computer simulations, we quantitatively determined the LFM contribution to the single-molecule spectra in our dye-matrix system at different temperatures.

Entanglement and quantal coherence: Study of two limiting cases of rapid system-bath interactions

In this paper, we consider the dynamics of a system coupled to a thermal bath, going beyond the standard two-level system through the addition of an energy excitation degree of freedom. Further extensions are to systems containing many fermions, with the master equations modified to take Fermi-Dirac statistics into account, and to potentials with a time-dependent bias that induce resonant avoided crossing transitions. The limit $\stackrel{\ensuremath{\rightarrow}}{Q}\ensuremath{\infty},$ where the interaction rate with the bath is much greater than all free oscillation rates for the system, is investigated. Two behaviors are possible: freezing (quantum Zeno effect) or synchronization (motional narrowing). We clarify the conditions that give rise to each possibility, making an explicit connection with quantum-measurement theory. We compare the evolution of quantal coherence for the two cases as a function of Q, noting that full coherence is restored as $\stackrel{\ensuremath{\rightarrow}}{Q}\ensuremath{\infty}.$ Using an extended master equation, the effect of system-bath interactions on entanglement in bipartite system states is computed. In particular, we show that the sychronization case sees bipartite system entanglement fully preserved in the large Q limit.

Infrared Spectral Hole-Burning and Spectral Diffusion ofVibrational N-D Bands in a Disordered Tutton Salt

We have studied infrared spectral hole burning of the N-D stretching bands ofNH3D+ in salt [(NH4)2Co0.25Ni0.75(H2O)6(SO4)2] at 10 K. We have observed that thespectral line broadening occurred on a logarithmic timescale,which is consistent with the theoreticalprediction of a standard two-level system. The temperature of 10 K is alsobeyond the temperature limit in previous studies on spectral diffusion.

Studies of relaxation processes in organic glasses at low temperatures using the hole-burning spectroscopy technique: Verification of applicability limits of the model of two-level systems

A vitreous state is originally nonequilibrium. Because of this, attempts to classify relaxation processes in glasses as equilibrium and nonequilibrium are, strictly speaking, incorrect. This classification is, however, possible and useful at low temperatures when the model of two-level systems (TLS) appears to be sufficient to describe properties of glasses. Until now, the question of the applicability limits of the TLS model has remained unclear both in the temperature and temporal domains. A number of deviations from the so-called standard TLS model, observed experimentally, can be easily accounted for with allowance for nonequilibrium effects considered as a result of the nonequilibrium state of the TLS ensemble. There are some effects, however, that cannot be consistently explained within the framework of the TLS model. In this paper, we briefly consider the results of studying the relaxation processes in organic glasses at low temperatures in a wide time range using the spectral hole-burning technique. The experimental data are compared with predictions of the TLS model, and spectral criteria for the limits of its applicability are proposed.

Spectral diffusion induced by sudden jump processes

A concise analytical method is given to describe the spectral diffusion in the system with several sudden jump modulators from the frequency domain viewpoint. Spectral diffusion of chromophores in low temperature glasses is investigated by this method with the standard two-level system model. Under the standard approximation, the spectral diffusion has exactly the same form as the stimulated photon echo result. The time-dependent heterogeneous line width increases as the logarithm of waiting time.

Are the spectral trails of single molecules consistent with the standard two-level system model of glasses at low temperatures?

The spectral trail of a single molecule is a 2D plot of many repeated spectra displayed as a function of time. Here, we present an analysis of the spectral trails of some 70 terrylene molecules in polymers. We compare the features of individual trails to the standard model of two-level systems (TLSs) in glasses at low temperatures, and we find a good overall agreement for a majority of molecules. However, more than 30% of the molecular trails cannot be reconciled with the standard model. For example, we found three-level systems, evidence for a strong coupling between some TLSs, and spectral drifts. Whereas our data confirm that the standard TLS model describes large ensembles of TLSs quite satisfactorily, this may result only from a cancellation of the deviations. Therefore, the application of the model to explain the spectral diffusion of individual molecules must be questioned in each particular case.

Are there charged two-level systems in polymers?

It is shown that a square-root temporal hole broadening found recently in polymethylmethacrylate (PMMA) over a time scale ranging from 10 3 to 10 6 s can be explained in the framework of the standard two-level system model with an additional assumption that only a small part (∼10 −11) of the two-level system existing in PMMA has a charge.

Does the standard TLS model fail to explain the experimental data on the long-lived stimulated photon echo in amorphous solids?

The formulae of dynamical spectral diffusion (SD) theory are used to treat the experimental data on the long-lived stimulated photon echo in amorphous solids. This theory is based on the standard two-level system model proposed by Anderson, Halperin, Varma and Phillips. Dynamical SD theory removes all the contradictions existing between the experimental data and stochastic SD theory for a long-lived stimulated photon echo.