Coherent Phonon States Research Articles

Phonon trapping states as a witness for generation of phonon blockade in a hybrid micromaser system

In a hybrid micromaser system consisting of an optical cavity with a moving mirror connected to a low temperature thermal bath, we demonstrate, both analytically and numerically, that for certain interaction times between a random atomic flux and the optomechanical cavity, vacuum phonon trapping states are generated. Furthermore, under the approach of the master equation with independent phonon and photon thermal baths, we show that the trapping of the phonons and photons is achieved for the same interaction times. The results also indicate that by increasing the cavity-oscillator coupling one may generate a coherent phonon state aside from the trapping states. Within the same hybrid system, but now connected to the squeezed phonon reservoir, a phonon blockade effect can be engineered. Moreover, we identify an interconnection between the trapping and blockade effects, particularly if one approaches the vacuum trapping state, strong phonon blockade can be achieved when the system is connected with a weakly squeezed phonon reservoir.

Photon scattering from a quantum acoustically modulated two-level system

We calculate the resonance fluorescence signal of a two-level system coupled to a quantized phonon mode. By treating the phonons in the independent boson model and not performing any approximations in their description, we also have access to the state evolution of the phonons. We confirm the validity of our model by simulating the limit of an initial quasi-classical coherent phonon state, which can be compared to experimentally confirmed results in the semiclassical limit. In addition, we predict the photon scattering spectra in the limit of purely quantum mechanical phonon states by approaching the phononic vacuum. Our method further allows us to simulate the impact of the light scattering process on the phonon state by calculating Wigner functions. We show that the phonon mode is brought into characteristic quantum states by the optical excitation process.

Cavity control of nonlinear phononics

Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly excited coherent infrared-active phonon state into the other vibrational degrees of freedom of the system. The hybridization of the infrared-active phonon mode with the fundamental mode of the cavity induces a polaritonic splitting that we use to tune the nonlinear interactions with other vibrational modes in and out of resonance. We show that not only can the efficiency of the redistribution of energy be enhanced or decreased, but also the underlying scattering mechanisms may be changed. This work introduces the concept of cavity control to the field of nonlinear phononics, enabling nonequilibrium quantum optical engineering of new states of matter.

Managing Quantum Heat Transfer in a Nonequilibrium Qubit-Phonon Hybrid System with Coherent Phonon StatesSupported by the National Natural Science Foundation of China (Grant No. 11704093), the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, the National Natural Science Foundation of China (Grant Nos. 11935010 and 11775159), and the Natural Science Foundation of Shanghai (Grant Nos.

We investigate quantum heat transfer in a nonequilibrium qubit-phonon hybrid open system, dissipated by external bosonic thermal reservoirs. By applying coherent phonon states embedded in the dressed quantum master equation, we are capable of dealing with arbitrary qubit-phonon coupling strength. It is counterintuitively found that the effect of negative differential thermal conductance is absent at strong qubit-phonon hybridization, but becomes profound at weak qubit-phonon coupling regime. The underlying mechanism of decreasing heat flux by increasing the temperature bias relies on the unidirectional transitions from the up-spin displaced coherent phonon states to the down-spin counterparts, which seriously freezes the qubit and prevents the system from completing a thermodynamic cycle. Finally, the effects of perfect thermal rectification and giant heat amplification are unraveled, thanks to the effect of negative differential thermal conductance. These results of the nonequilibrium qubit-phonon open system would have potential implications in smart energy control and functional design of phononic hybrid quantum devices.

Impact of counter-rotating-wave term on quantum heat transfer and phonon statistics in nonequilibrium qubit–phonon hybrid system* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11704093, 11775159, and 11935010), the Natural Science Foundation of Shanghai, China (Grant Nos. 18ZR1442800 and 18JC1410900), and the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology.

Counter-rotating-wave terms (CRWTs) are traditionally viewed to be crucial in open small quantum systems with strong system–bath dissipation. Here by exemplifying in a nonequilibrium qubit–phonon hybrid model, we show that CRWTs can play the significant role in quantum heat transfer even with weak system–bath dissipation. By using extended coherent phonon states, we obtain the quantum master equation with heat exchange rates contributed by rotating-wave-terms (RWTs) and CRWTs, respectively. We find that including only RWTs, the steady state heat current and current fluctuations will be significantly suppressed at large temperature bias, whereas they are strongly enhanced by considering CRWTs in addition. Furthermore, for the phonon statistics, the average phonon number and two-phonon correlation are nearly insensitive to strong qubit–phonon hybridization with only RWTs, whereas they will be dramatically cooled down via the cooperative transitions based on CRWTs in addition. Therefore, CRWTs in quantum heat transfer system should be treated carefully.

Magneto-transport properties of a single molecular transistor in the presence of electron-electron and electron-phonon interactions and quantum dissipation

A single molecular transistor is considered in the presence of electron-electron interaction, electron-phonon interaction, an external magnetic field and dissipation. The quantum transport properties of the system are investigated using the Anderson-Holstein Hamiltonian together with the Caldeira-Leggett model that takes care of the damping effect. The phonons are first removed from the theory by averaging the Hamiltonian with respect to a coherent phonon state and the resultant electronic Hamiltonian is finally solved with the help of the Green function technique due to Keldysh. The spectral function, spin-polarized current densities, differential conductance and spin polarization current are determined.

Influence of excited state decay and dephasing on phonon quantum state preparation

The coupling between single-photon emitters and phonons opens many possibilities to store and transmit quantum properties. In this paper we apply the independent boson model to describe the coupling between an optically driven two-level system and a discrete phonon mode. Tailored optical driving allows not only to generate coherent phonon states, but also to generate coherent superpositions in the form of Schr\"odinger cat states in the phonon system. We analyze the influence of decay and dephasing of the two-level system on these phonon preparation protocols. We find that the decay transforms the coherent phonon state into a circular distribution in phase space. Although the dephasing between two exciting laser pulses leads to a reduction of the interference ability in the phonon system, the decay conserves it during the transition into the ground state. This allows to store the phonon quantum state properties in the ground state of the single-photon emitter.

Coherent and squeezed phonons in single wall carbon nanotubes

Coherent states of phonon manifest in macroscopic beatings of reflectance or transmittance following the phonons frequencies when a material is excited with an ultrashort pulse. Such beatings predominantly arise from a single phonon excitation. The two-phonon (overtone or combination modes) excitations, such as the G′ (or 2D) band phonons in single wall carbon nanotubes (SWNTs), on the other hand, are not compatible with the coherent phonon states picture. Nevertheless, their macroscopic beatings are observed in the experiment. Here we formulate a more general framework involving the so-called squeezed states of phonon to explain the origin of the two-phonon signals in the pump-probe experiment of SWNTs. For a given SWNT chirality, the G′ band phonon intensity in terms of the squeezed states of phonons is compared with that in terms of coherent states of phonons. Our calculation reveals that the G′ band intensity from the squeezed states of phonons is some orders of magnitude larger than that from the coherent states of phonons. We also compare the G′ band phonon intensity with the intensities of other coherent phonon modes generated in ultrafast spectroscopy such as the G band. Furthermore, the coherent G band and squeezed G′ band phonon intensities are found to be sensitive to the laser pulse width used in ultrafast spectroscopy.

Infrared Problem in Cold Atom Quantum Physisorption on 2D Materials

Results from four different approximations to the phonon-assisted quantum adsorption rate for cold atoms on a 2D material are compared and contrasted: (1) a loop expansion (LE) based on the atom-phonon coupling, (2) non-crossing approximation (NCA), (3) independent boson model approximation (IBMA), and (4) a leading-order soft-phonon resummation method (SPR). The SPR method treats the adsorbed atom as a surface polaron where the phonon cloud accompanying the bound atom is a phonon coherent state. We conclude that, of the four approximations considered, only the SPR method gives a divergence-free result in the large membrane regime at finite temperature. The other three methods give an adsorption rate that diverges in the limit of an infinite surface.

Gravitational waves and coherent phonon states in elastic media: 1D-analysis

Longitudinal acoustic phonons in a one-dimensional elastic string are studied in the field of a weak gravitational wave. Working in the analogue gravity framework, a lagrangian describing longitudinal wave propagation along the string is derived in the background of a suitable acoustic metric, the latter encoding both the spacetime corrections due to the gravitational wave and the elastic properties of the string. After quantization, a phonon Hamiltonian is obtained, having the structure of the Luttinger liquid Hamiltonian. Such Hamiltonian is subsequently employed to analyze some effects induced by a gravitational wave, as time evolution of phonon vacuum state, gravitational vacuum squeezing and time evolution of two-mode choerent phonon states, with particular concern to ionic density fluctuations. These findings are in good agreement with similar results appeared in the literature, although in quite different material media. This suggests that the above cited effects do represent a quite general manifestation of the peculiar response to gravitational waves in macroscopic particle ensembles whose internal structure admits some kind of wave propagation.

Phonon impacts on entangled photon pair generation from the biexciton cascade in a quantum dot: phonon coherent state representation

A full quantum microscopic theory is developed to analyze a biexciton radiative cascade coupled to bulk acoustic phonons in a quantum dot. By considering the phonon sub-system in coherent state representation a new approach is proposed for investigating the phonon effects. Via this approach it is possible to obtain an exact analytical result for the phonon kernel in this system. This approach is introduced in the context of an example: the process of generating polarization-entangled photon pairs from the biexciton cascade in a quantum dot. We calculate the exact density matrix (using quantum state tomography) of photons and their concurrence. We show that the exchange interaction and temperature have remarkable effects on the degree of entanglement of the emitted photons. The approach introduced provides an exact analytical result for finite discrete electron states interacting with phonons.

Dynamics of a Strongly Coupled Polaron

We study the dynamics of large polarons described by the Froehlich Hamiltonian in the limit of strong coupling. The initial conditions are (perturbations of) product states of an electron wave function and a phonon coherent state, as suggested by Pekar. We show that, to leading order on the natural time scale of the problem, the phonon field is stationary and the electron moves according to an effective linear Schroedinger equation.

Phonon-induced effects on exciton dynamics and photon emission from a semiconductor quantum dot microcavity: phonon coherent state representation

A microscopic theory to study the combined dynamics of a quantum dot exciton coupled to a single cavity mode as well as acoustic phonons is presented. By considering the phonon subsystem in the coherent state representation, the phonon’s impact on the emitted photons is investigated. The single photon emission probability and phonon effects on this quantity are studied. On the other hand, we illustrate that while a quantum dot interacts with a single cavity mode, the collapse and revival phenomenon will occur. It is demonstrated that acoustic phonons have a pronounced impact on the collapse and revival of the quantum dot exciton. Our finding reveals that at elevated temperatures the phonon interaction decreases the Rabi frequency. Moreover, the cavity mode possesses non-classical features such as sub-Poissonian statistics.

Quantum transport of double quantum dots coupled to an oscillator in arbitrary strong coupling regime

In this paper, we investigate the quantum transport of a double quantum dot coupled with a nanomechanical resonator at arbitrary strong electron-phonon coupling regimes. We employ the generalized quantum master equation to study full counting statistics of currents. We demonstrate the coherent phonon states method can be applied to decouple the electron-phonon interaction non-perturbatively. With the help of this non-perturbative treatment of electron-phonon couplings, we find that the phonon-assisted resonant tunneling emerges when the excess energy from the left quantum dot to the right one can excite integer number of phonons and multi-phonon excitations can enhance the transport in strong electron-phonon coupling regime. Moreover, we find that as the electron-phonon coupling increases, it first plays a constructive role to assist the transport, and then plays the role of scattering and strongly represses the transport.

Nonclassical ground state for Fröhlich palaron

Based on the variational approach proposed by Huybrecht , using the two-mode squeezed coherent state as the second-step canonical transformation, we have investigated the nonclassical ground state for the Fröhlich polaron through considering the dynamical correlation bewteen the phonon wave vectors q and q' . Due to the correlation effect between the phonon coherent state and the phonon squcezed state, caused by the two-mode squeezing effect of the phonon coherent state, the coherent parameter fq and the two-mode squeezing angle φqq' also have a big correction correspondingly. As a result , this effect has greatly enhanced the coherent effect and the squeezing angle effect . The calculation and the analysis based on the ground state energy of the polaron have shown that 1) for the weakly coupled region ,the correction ΔE(1)c due to the effect of the displaced-phonon squcezed state is comparable to the Feynma n' s path integral calculation (ΔEf) and the coherent state correetion by Huybrechts (ΔE0), while the correction (ΔE(2)c) due to the squeezing effect of the phonon coherent state has an essential contribution , i.e. ΔE(2)c«(ΔEf,ΔE0); 2) for the strongly-coupled region ,the contribution from the displaced-phonon squcezed state has a greatly reduction , ΔE(1)c≥(ΔEf,ΔE0) .Althougth, at the same time ,the contribution due to the squeezing effect of the phonon coherent state also has a greatly reduction ,we still have ΔE(2)c«(ΔEf,ΔE0).

Non-classical state effect on the persistent current in one-dimensional mesoscopic ring with electron-phonon interaction

Based on the efficacy of the phonon coherent state and with consideration of the non-classical effect of the squeezed state of phonon, the influence of the electron-magnon interaction and the electron-phonon interaction on the persistent current in one-dimensional mesoscopic ring is studied. Compared with the free ring, our study shows that in one-dimensional mesoscopic ring, the amplitude of the persistent current exponentially diminishes due to the electron-magnon interaction. For the normal state electron, the interaction of the electron-phonon causes the persistent current to weakendce to the Debye-Waller effect. However, taking the correlation between the hopping electron states and the one-phonon coherent states into the equation, the ground energy of the mesoscopic system is declined in a large scale. In result, the persistent current In is increased substantially. On the other hand, taking the behavior of the two-phonon coherent state into account, as the effect of the squeezed states of phonons maintains the phase coherence of electrons, so the Debye-Waller attenuation is weakened effectively. Especially, when the squeezed angle is larger, because of the non-adiabatic correlation between the squeezed-phonon states and the coherent states of phonon, it causes a significant decline in the ground state energy and a significant increase in the squeezed angle, thus persistent current has a even more significant increase. It should be pointed out, that the persistent current shows period oscillation as the external magnetic flux changes. Even the external magnetic flux Φem=0, still the persistent current of the intrinsic has I ~ n≠0. The system continuoues to support the equilibrium spin and charge flow, the external magnetic flux only plays the role of an adiabatic parameter.

Fluctuation properties of phonons generated by ultrafast optical excitation of a quantum dot

AbstractIn this paper, the fluctuation properties of phonons after the optical excitation of a quantum dot with an ultrashort laser pulse are studied theoretically. When a single pulse with pulse area π creates an exciton in the system, a coherent phonon state builds up. Fluctuations of coherent states are time independent and equal to the vacuum fluctuations. By an excitation with a π/2 pulse a superposition of ground and exciton state is created. In this case the phonon system becomes entangled with the electronic system. In the phonon subsystem this leads to the formation of a statistical mixture of the vacuum and the coherent state. The fluctuations of this mixture oscillate in time with both the single and the double phonon frequency, but never exhibit squeezing. The discrepancies with the predictions made in a Raman tensor model are briefly discussed. All scenarios are illustrated using the Wigner function.

Entanglement of three-level trapped ions with phonon trap modes

The entanglement between a single electron in the electronic states of a trapped three-level ion and the ionic vibrational modes of the trap is studied for an initially unentangled state of an electron level and a coherent phonon state. The effects of time-independent and time-dependent couplings are discussed.

Bismuth under intense laser pulses: a Fano-like interference description

New time-resolved experiments by Misochko et al published in a recent issue of J. Phys.: Condens. Matter [1] have furthered our understanding of the complex behaviour of Bi far from equilibrium. There has been a long-standing interest in the dynamical path from a coherent to a stochastic state. In 1955, Fermi, Pasta, and Ulam (FPU) [2] numerically tested the ergodicity hypothesis of statistical mechanics. By considering a chain of classical harmonic oscillators coupled with a quadratic nonlinearity they investigated how the energy in one mode spreads to the rest. The study was performed on the fastest computing machine at the time (MANIAC I at Los Alamos). Surprisingly, instead of a gradual, continuous flow of energy from the first vibrational mode to the higher modes, FPU found that the system cycled periodically, i.e. after a while the first mode was revived. Nowadays, the availability of intense femtosecond laser pulses in small-scale laboratories enables the generation and study of coherent phonon states in real materials. Particularly interesting for applications are the large-amplitude phonons, as they can offer a unique way to manipulate lattice structures and shapes [3]. However, understanding large-amplitude coherent dynamics is a difficult task, as it involves both electronic and ionic degrees of freedom departing from their ground state. Bi is an interesting system to probe. It is a semimetal that exhibits a delicate coupling between its electronic and ionic subsystems. This is evidenced by its α-arsenic A7 crystal structure, which is an almost perfect cubic structure with a slight elongation along the (111) diagonal (figure 1). The origin of this distortion is the Peierls effect, which is most commonly encountered in one-dimensional systems. In the report of Misochko et al [1], two coherent modes of different symmetries are excited and studied: a fully symmetric A1g mode, where atomic motion occurs along the Peierls distortion direction, and a degenerate Eg mode, where motion occurs in the perpendicular plane (figure 1). Various time-resolved studies on the Bi response obtained that low-amplitude coherent phonon dynamics showed the expected decay and thermalization. However, for abovethreshold excitations, the recurrent dynamics of coherent phonons reminds one of the celebrated FPU paradox, showing a collapse and revival in the A1g mode [4]. Such nonlinear behaviour brings into attention both lattice anharmonicity [5] and dynamical screening effects [6]

Coherent-phonon vibronic sideband

We present the theory of vibronic sideband spectra due to coherent phonon modes using the conventional model of linear electron–phonon coupling and displaced equilibrium positions of the oscillators in the exited and final electronic states. Unlike in the conventional theory the initial state of the oscillator is taken as a coherent phonon state and not as a thermalized one. Under these conditions we got an exact analytical solution for the lineshape of the vibronic sideband. The sideband is determined by two parameters, the Huang–Rhys parameter S and the coherence parameter α of the phonon state. For α=0 the lineshape converts into the standard Pekarian form for T=0.