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Letter Cite This: Nano Lett. XXXX, XXX, XXX−XXX

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Coherent Discriminatory Modal Manipulation of Acoustic Phonons at the Nanoscale Shang-Jie Yu†,‡ and Min Ouyang*,† †

Department of Physics and Center for Nanophysics and Advanced Materials and ‡Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, United States S Supporting Information *

ABSTRACT: Understanding and controlling the phononic characteristics in solids is crucial to elucidate many physical phenomena and develop new phononic devices with optimal performance. Although substantial progress on the spatial control of phonons by material design has been achieved, the manipulation of phonons in the time domain has been less studied but can elucidate in-depth insight into various phonon-coupling processes. In this work, we explore different time-domain pumpcontrol(s)-probe phonon manipulation schemes in both simulations and experiments with good consistency. In particular, we use an Au−Ag core−shell nanoparticle with a manifestation of multiple phonon vibrational modes as a model system for multimodal-phonon manipulation, and we demonstrate that the simple addition of a femtosecond optical control pulse to an all-optical pump−probe phonon measurement can enhance or suppress the fundamental breathing phonon mode of nanoparticles depending on the time separation between the pump and the control pulses. A more advanced control of the higher-order phonon modes and their interplay has also been achieved using two sequential and independently tunable optical control pulses, which enables the discriminatory modal manipulation of phonons for the first time. This work represents a significant step toward a deep understanding of the phonon-mediated physical and chemical processes and a development of new nanoscale materials with desirable functionalities and properties. KEYWORDS: Phonon manipulation, phonon modes, ultrafast optical spectroscopy, finite element method simulation

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potential to offer a precise control of phonon engineering in the spatial domain.15−17 Nevertheless, a phonon is inherently dynamic in the time domain, and the phononic excitation can be achieved in a time scale of femtoseconds (fs) or picoseconds (ps) through different mechanisms,12,13 thus providing a unique method to coherently manipulate the phonon vibrations when the process is much faster than characteristic quantum dissipation time. Until now, although evidence of the suppression of the fundamental breathing mode of spherical nanoparticles was observed in an ultrafast optical study,18 a systematic investigation to understand the in-depth mechanisms or more advanced control of phonons has been absent. Here, we use the recently developed bimetallic core−shell nanostructures, whose phonon modes can be precisely tailored through an acoustically mismatched core−shell interface,15,19 as a model system to demonstrate the feasibility of the discriminatory multimodal manipulation of phonons at the nanoscale. First, we use the finite-element method (FEM) simulation to demonstrate that the sequential application of impulsive excitations of acoustic phonons can be used to control the phonon modes in a coherent and highly selective manner. From the classical perspective, such phononic control schemes can be understood as the constructive and destructive

honons play a key role in almost every physical process in condensed matter, for example, decoherence of quantum states, electronic transport, and thermal management.1,2 Understanding or controlling phonons and associated dynamics should be crucial to elucidate many underlying physical mechanisms/processes, optimize the device performance and create new device concepts.3−8 Indeed, progress has recently been made toward achieving phononic control, mainly by material design. For example, a few state-of-the-art mesoscopic phononic devices and complex phononic structures, including phononic resonators9,10 and thermal rectifiers,11 have drawn substantial attentions because of their unique capability to guide the phonon propagation. In particular, using the size confinement and shape control, the phononic characteristics of one material (e.g., phonon dispersion and group velocity) can be dramatically modified at the nanoscale, which offers a new method to finely engineer the phonon spectra that cannot be available in their bulk counterparts. This includes the appearance of discrete quantized acoustic phonon modes in a nanostructure because the translational invariance is broken (e.g., different orders of the symmetric breathing phonon modes have been extensively observed for spherical nanoparticles), and the multimodal frequencies have shown distinct dependence on the size and shape of nanostructure.12−14 When combined with recently developed materials at the nanoscale, the phononic modulation through intimate interfacial coupling in a hybrid nanostructure has been achieved and has the © XXXX American Chemical Society

Received: November 2, 2017 Revised: January 3, 2018

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DOI: 10.1021/acs.nanolett.7b04662 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters interference of multiple impulsively excited phononic waves with the prediction of the monotonic modulation of phonon vibrational amplitude by varying the time interval between the excitation pulses. Importantly, when a dual control pulse scheme is used, different phonon modes can be selectively enhanced or annihilated by controlling the combinations of two sequential control pulses. Experimentally, these coherent discriminatory multimodal phonon manipulations should be achievable by designing and using a set of femtosecond optical pulses in an ultrafast optical study. In our current work, we further experimentally demonstrate the monotonic modulation of the fundamental phononic mode in a simple single-control pulse scheme and more selective control of different higherorder phononic modes in a complex dual-control pulse scheme, which is consistent well with the FEM simulations. This work highlights the feasibility of the in situ ultrafast phononic control in a highly selective manner in the time domain. This control opens up new and exciting avenues to understand and manipulate phonon-mediated physical and chemical processes with insight into the roles of specific phonon modes when we integrate with other experimental techniques,20−23 which is notably challenging otherwise. Figure 1a shows a schematic of the coherent phonon control in the time domain from the wave perspective. Phonon vibrations can be impulsively launched in a nanoscale atomic lattice with broadly distributed modes (denoted by n = 0, 1, 2..., where n is the quantization mode number) that manifest

distinct frequencies, phases and amplitudes. Typically, the fundamental mode (n = 0) has larger vibrational strength than higher-order modes (n ≥ 1) in a broadband phonon excitation. Following this initial phonon excitation, a second short pulse (termed “control pulse”) can be introduced to coherently interact with the existing phonon vibrations, which redistributes the mode energy. When the widths of the excitation and control pulses are sufficiently short, the relative phase of a specific phonon mode can be precisely tuned under sequential excitations, which causes modal enhancement or annihilation. This wave perspective and phase control concept can be further extended to a more complex and selective phonon manipulation by designing an advanced sequence of independent phonon excitation pulses. The classical continuum mechanics with FEM simulation can be applied to nanoscale structures to understand their acoustic phonon characteristics, which is consistent with experimental results.15,24,25 Therefore, we used the time-domain FEM simulation to implement and evaluate the proposed phonon manipulation schemes in Figure 1a. Briefly, in our simulation, a uniform impulsive force with fs-pulse width is applied to the nanoparticle with an isotropic elasticity to excite acoustic phonons, and its time-dependent surface displacement is computed and recorded as a signal of phonon vibrations (see more details in the Supporting Texts and Table S1 for simulation parameters). In particular, we selected an Au−Ag core−shell nanostructure as a model system (Figure 1b) for our current work because prior work has demonstrated that this type of nanostructure can enable a precise engineering of a series of phonon modes by tailoring the interfacial acoustic coupling,15 which represents an ideal system to demonstrate the multimodal phonon manipulation as illustrated in Figure 1a. Figure 1c presents a computed two-dimensional map of the time-dependent phonon oscillation in the single-control pulse scheme, where a second impulsive phonon excitation (as control) is applied after initial excitation with a time interval of Δtcon. By sweeping Δtcon, clear suppression and enhancement of phonon vibration are observed, depending on the specific value of Δtcon. The Fourier transform (FT) analysis of the computed time-dependent phonon dynamics shows that the fundamental mode is dominant under such impulsive excitation, and a clear and strong modulation of this specific phonon mode is revealed, whereas the variation in higher-order modes is relatively weak in the single-control pulse scheme (Figure S1). We have further evaluated a more complex control scheme that consists of dual-control pulses, where the time interval of each control pulse relative to the initial excitation pulse (i.e., Δtcon1 and Δtcon2) can be independently tuned. A few exemplary maps of the computed phonon dynamics under different combinations of Δtcon1 and Δtcon2 are presented in Figure S2, which shows more complicated phonon dynamic features in this dual-control pulse scheme. To evaluate the effects on different phonon modes in this manipulation process, we computed and compared the vibrational amplitudes of three different phonon modes (n = 0, 1, 2) as a function of Δtcon1 and Δtcon2 and present the results in Figure 1d. For each phonon mode n, there is a periodic modulation of the phonon vibration amplitude as a function of Δtcon1 and Δtcon2, which originates from the harmonic nature of the acoustic vibrations, but the modulation pattern clearly depends on the phonon mode because of the difference in their inherent phonon frequencies. Compared with the computational results from the singlecontrol pulse scheme, one immediate implication of Figure 1d

Figure 1. FEM simulation of discriminatory modal phonon manipulation. (a) Schematic of the coherent discriminatory phonon manipulation by the impulsive phonon excitation. (b) Model of a core−shell nanostructure to allow the precisely engineered phonon spectra that can be desirable for phonon manipulation. (c) FEMcomputed phonon control via a single-control pulse scheme. A twodimensional map of the phonon vibrational dynamics is plotted by varying Δtcon of the control pulse with respect to the initial phonon excitation at t = 0. The color bar is the normalized phonon intensity (to maximum phonon amplitude). (d) FEM-computed phonon control via a dual-control pulse scheme. The two-dimensional FT amplitude maps of the FEM-computed phonon dynamics after application of two sequential control pulses are plotted for three distinct phonon modes, respectively. For clarity, the FT amplitude maps of modes n = 1 and n = 2 are shifted up vertically by two and four units, respectively. B

DOI: 10.1021/acs.nanolett.7b04662 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters is that by judiciously selecting a combination of Δtcon1 and Δtcon2, one specific phonon mode can be enhanced or suppressed, which causes the discriminatory modal control of phonons, or a more general design of the phonon modal spectra that consists of only desirable modes. Figure S3 shows some examples to highlight this discriminatory modal control of the n = 0, 1, and 2 modes, respectively, which can be enabled by selecting different combinations of Δtcon1 and Δtcon2. Two time-domain animations (Movies S1 and S2) of the discriminatory modal control of the n = 0 and n = 1 modes clearly illustrate the effects of our proposed dual pulse control scheme, where the selective combination of two control pulses creates the unadulterated sinusoidal phonon vibration with a dominant mode. Experimentally, there are some challenges to realize phonon control as illustrated and predicted in Figure 1. First, an impulsive mechanism to excite phonons is required in a significantly shorter time scale than the related energy redistribution. Second, the availability of multiple pulses with precise control of relative time separation is desirable to achieve the tunability and gain an understanding of the manipulation process. Third, an extremely sensitive and in situ technique to probe the variation in phonon dynamics in the time domain should be crucial while performing the phonon manipulation; finally, from a material standpoint exceptional sample quality is required to achieve a sufficiently long phonon coherence time and a suitable vibrational frequency to enable the application of a pulse sequence before the phononic decoherence occurs. Figure 2a shows a schematic of an experimental pumpcontrol(s)-probe setup based on femtosecond time-resolved spectroscopy. It has been demonstrated that the broadband impulsive excitation of phonons can be uniquely achieved using an ultrafast laser with extremely short pulse width through the optical excitation of electrons at the Fermi energy and a subsequent electron−phonon (e-ph) coupling process.3,12,15,26 In our apparatus, up to four ultrafast coherent optical pulses with pulse widths of ∼70 fs can be sequentially delivered to the sample with independent control of their arrival time, pulse intensity and photon energy to take different roles for the phonon excitation (pump pulse), phonon manipulation (control pulse(s)) and phonon detection (probe pulse) (see Supporting Methods). We observe that the impulsive phonon excitation is less dependent on the pump photon energy if it is sufficiently high for the optical excitation of electrons.3,15 As a result, in our phonon manipulation experiments the pump and control pulses are always set to have identical photon energies but with independently tunable power; however, the photon energy of the probe pulse is typically set to be different and always tuned to maximize the phonon detection signal. Briefly, the electronic temperature of the sample is substantially increased and quickly equalized (less than 0.5 ps) after the absorption of an ultrafast photon pulse because of the electron−electron (e-e) scattering. The energy of hot electrons can be redistributed and exchanged to the atomic lattice typically within a few ps through the e-ph coupling, which induces an impulsive excitation process of phonons. Furthermore, the coherently excited vibrational motion of the lattice periodically oscillates the volume of the nanostructures, which modulates the electronic and optical properties that can be detected by monitoring the transient absorption/transmission trace and offers a detection mechanism of phonons in the time domain. The detection sensitivity can be dramatically improved by using a lock-in technique with differential

Figure 2. Experimental all-optical setup and the Au−Ag core−shell nanostructures for the coherent phonon manipulation. (a) Schematic of an all-optical experimental setup that consists of up to four sequential optical pulses in the time domain. The lock-in detection technique is applied by modulating different optical paths with different frequencies, f i (i = 1, 2, 3, and 4) to probe weak phonon signal. (b) A typical TEM image of the Au−Ag core−shell nanostructures that consists of the Au core (3.8 ± 0.2 nm) and four monolayers of the Ag shell (0.9 ± 0.2 nm). Scale bar, 20 nm. (Inset) High-resolution TEM image highlighting the core and shell configuration. The red and yellow dashed lines are guides for the core- and shell- boundaries, respectively. Scale bar, 5 nm. (c) Typical normalized experimental differential optical transmission (ΔT/T) as a function of time delay of probe (Δtprobe) that is acquired from the sample in (b). The impulsive phonon excitation and relaxation with characteristic time scale can be identified. (d) (Left) Experimental signal of phonon dynamics after 5 ps by subtracting the data in (c) from an exponential damping background. The red solid line is a fit with a damped sinusoidal function of amplitude to this experimental data as described in the Supporting Information. (Right) The FT spectra of the phonon oscillation traces on the left, which shows three detected phonon modes that are highlighted by arrows.

frequency modulations of the optical pulses. The combination of these processes can satisfy the experimental requirements for the phonon manipulation schemes presented in Figure 1. We applied an optical scheme in Figure 2a to Au−Ag core− shell nanoparticles with intrinsic acoustic phonons and multiple modal frequencies in the regime accessible by optical methods. Figure 2b shows a typical electron microscopy characterization of the Au−Ag core−shell nanoparticles in this work, which highlights their size uniformity, which is a prerequisite for the optical generation and manipulation of multimodal phonons. Because the size of the core−shell nanostructures is notably uniform and significantly smaller than the laser focus spot size (∼50 μm in our experiment) and optical penetration depths of both Au and Ag, the impulsive optical excitation of nanostructures can be considered uniform under the far-field and ensemble measurement conditions. Figure 2c shows a C

DOI: 10.1021/acs.nanolett.7b04662 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters typical time-resolved differential optical transmission spectrum (ΔT/T) without control pulses, which clearly highlights the intercorrelated energy coupling process with different characteristic time scales that are suitable for impulsive phonon excitation and phonon detection in the time domain. A more detailed analysis of the impulsive phonon excitation through the e-ph coupling mechanism can be found in Figure S4. A clear oscillatory behavior after 5 ps can be identified after removing the fitted background signal with an exponential function (Figure 2d). Its corresponding FT spectroscopy unambiguously reveals the existence of three detected phonon modes, which can be assigned as breathing phonon vibrations with n = 0, 1, and 2. This result is consistent with the FEM simulation (Figure S1a) and validates our model in Figure 1. To ensure that our optical observations and manipulations (as presented below) are not caused by photon-induced damages because of optical heating or sample degradation, we regularly checked the sample quality after the optical measurements and confirmed that we did not observe any evidence of sample change in the current optical study (Figure S5). Figure 3 summarizes the experimental results of the implementation of one single-control pulse scheme. Figure 3a is a two-dimensional map of phonon dynamics when only the relative time separation between the control and the pump pulses (Δtcon) is varied, whereas other experimental parameters such as the pulse intensity remain unchanged. A strong monotonic modulation of the phonon oscillations as a manifestation of the enhanced and reduced phonon amplitude is clearly observed when Δtcon is swept through one apparent oscillatory period, which is qualitatively consistent with the FEM simulation result (Figure 1b). Although the suppression of the fundamental phonon mode of the spherical metal nanoparticles has been reported,18 the dependence of the phonon manipulation on Δtcon has not been achieved but is crucial for the in-depth understanding of phonon manipulation. To show the experimental relationship among different phonon modes in this single-control pulse scheme, three selected timedomain spectra from Figure 3a and their corresponding FT spectra are compared in Figure 3b. By comparing with the phonon dynamics in the absence of a control pulse (red curve), the phonon oscillation can be increased by approximately four times (green curve) or reduced to be almost untraceable (blue curve), which explicitly depends on the preselected value of Δtcon. Further comparison of their corresponding FT spectra uncovers a fine difference among these three different phonon modes in this single-control pulse scheme: the fundamental n = 0 mode is most dramatically modulated, but the higher-order ones are not (see also Figure S6 and Table S2). Thus, our single-control pulse scheme can be applied to selectively amplify or suppress the fundamental phonon modes in a highly controlled manner without substantial perturbation of the higher-order modes. Because different phonon modes have different characteristics and roles in a phonon-associated physical process, it is necessary to manipulate the fundamental mode and fine interplay between higher-order modes. To coherently control the finer interplay among different phonon modes, we further develop a complex dual-control pulses scheme as proposed in Figure 1d, and the results are shown in Figure 4. The interpulse separations Δtcon1 and Δtcon2 of two control pulses can be independently controlled relative to the initial pump pulse. The modulation of phonon dynamics in this control scheme is much more complicated and intuitively depends on the temporal

Figure 3. Experimental phonon manipulation via a single-control pulse scheme. (a) (Top) Schematic sequence of three optical pluses (pumpcontrol-probe) in the time domain. (Bottom) Experimental twodimensional map of the time-resolved phonon dynamics (after 5 ps) as a function of Δtcon. For comparison, two phonon dynamics spectra that are acquired before and after the application of the control pulse are plotted on the top and bottom of map, respectively. Two orange vertical arrows show the tuning range of Δtcon of the control pulse in this measurement. (b) (Left) Three selected traces from the map in (a) are presented: red, no control pulse; green, Δtcon = 9.25 ps; blue, Δtcon = 9.87 ps. Their corresponding positions in the two-dimensional map in (a) are highlighted by arrows with the same assignment of color code. (Right) Corresponding FT spectra of three phonon dynamic traces shown on the left. For clarity, the green and blue spectra are shifted up vertically by 0.06 and 0.28, respectively. However, the scale of each spectrum remains unchanged to compare their peak amplitude. Three vertical dash-dot lines highlight the frequencies of phonon modes n = 0, 1, 2.

combination of Δtcon1 and Δtcon2. Although a thorough experimental understanding of the synergistic interactions among multiple optical excitations is under investigation, a clear control of the fine interplay among different phonon modes is evident from selective results in Figure 4. Figure 4 particularly highlights that in this series of phonon control, the intensity of the n = 0 phonon mode is continuously reduced, whereas the intensity of the n = 1 mode is enhanced (see also Table S3). This result is different from our observation of the single-control pulse scheme, where the fundamental n = 0 mode is dominantly modulated (Table S2); thus, the promising control of the fine interplay among phonon vibrations is achievable in a dual-control pulse configuration. With the prediction from Figure 1d, our experimental apparatus in D

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because there is no efficient experimental approach to manipulate the phonon modes in a highly selective manner. Therefore, the discriminatory modal manipulation of phonons in our current work should help to differentiate the distinct roles of phonon modes. In particular, our phonon manipulation schemes are based on the ultrafast all-optical methodology. Ultrafast optical spectroscopy has also been used to study a wide range of physical phenomena, including spin and exciton dynamics,29−33 which offer a seamless integration with all optical phononic manipulations in our current work to uncover the roles of phonons and to control the diverse phonon-assisted physical processes. Lastly, but importantly, recent material advances have enabled the refined control of nanostructures with precisely engineered phonon characteristics.3,34,35 Therefore, combining a fundamental understanding of phonon modes with material advances should lead to a new design guideline for nanostructures to have optimized properties and functionalities.

Figure 4. Experimental phonon manipulation via a dual-control pulse scheme. (Top) Schematic sequence of four optical pluses (pumpcontrol-control-probe) in the time domain. (Bottom left) Three selected phonon dynamics spectra that show the effects of different combinations of Δtcon1 and Δtcon2. Red: no control pulse. Magenta: Δtcon1 = 7.56 ps and Δtcon2 = 7.68 ps. Wine: Δtcon1 = 8.47 ps and Δtcon2 = 8.74 ps. (Bottom right) The corresponding FT spectra of three data in the bottom left with the same assignment of color code. For clarity, the magenta and wine FT spectra are shifted up vertically by 0.08 and 0.12, respectively. However, the scale of each spectrum remains unchanged to compare their peak amplitude. Three vertical dash-dot lines highlight the frequencies of phonon modes n = 0, 1, 2.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04662. Simulation and experimental methods, supporting figures (Figures S1−S6), supporting tables (Tables S1−S3), and supporting texts. (PDF) Animation of a dual-pulse phonon control to selectively enhance the n = 0 phonon mode (AVI) Animation of a dual-pulse phonon control to selectively enhance the n = 1 phonon mode (AVI)

Figure 2a should enable considerably flexible control of different phonon modes, which cannot be achieved otherwise. In conclusion, we have performed the FEM simulation to evaluate different phonon manipulation schemes and show that distinct phonon modes of nanostructures can be manipulated in a coherent and highly selective manner according to the judicious design of a sequence of impulsive phonon excitations. Experimentally, this impulsive phonon excitation sequence can be realized by a train of femtosecond optical pulses. We have further designed and achieved different all-optical coherent phonon manipulations with results that are qualitatively consistent with the FEM simulation. Importantly, we first reveal that the manipulation scheme with dual control pulses should be sufficient to allow flexible control of the phonon modes in a highly selective manner. This all-optical phonon manipulation method is universal and can be readily applied to other materials, as long as their phonon decoherence time is long enough to allow application of pulse sequence. Future work that finely controls a few other experimental parameters such as the phase, photon energy, and intensity of the control pulses, should enrich this all-optical phononic control scheme. Our current simulation and experimental results of the discriminatory modal manipulation of nanoscale phonons have immediately opened up exciting research opportunities. First, phonon vibration is one of the most important subjects in the field of condensed matter physics. The coherent manipulation of phonons in the time domain can elucidiate different phonon relaxation and decoherence mechanisms in real time. Second, phonons play a key role in almost every physical and chemical process with important technology applications, which range from quantum information processing to energy conversion and transport.27,28 While understanding the roles of phonons in various processes has been intensively studied from both theoretical and experimental viewpoints, the differentiation of distinct phonon modes specifically in the relevant process has been lacking mainly

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Min Ouyang: 0000-0002-1721-1571 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge funding from NSF award (DMR1608720), ONR awards (N000141712885 and N000140710787), and Research Corporation (4330110). We also thanks facility support from Center for Nanophysics and Advanced Materials (CNAM), Maryland Nanocenter and its NISP laboratory (the NISP laboratory is supported in part by the NSF as MRSEC shared experimental facility).

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DOI: 10.1021/acs.nanolett.7b04662 Nano Lett. XXXX, XXX, XXX−XXX