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arXiv:2508.06683

Interference Between Electromagnetic and Mechanical Waves

Alexandre C. Ricardo, Ciro Micheletti Diniz, Celso J. Villas-Bôas

Published Aug 8, 2025• 0 citations
arXivHTMLPDF

Abstract

Classically, wave interference is a phenomenon that can be explained by considering only the waves themselves, that is, without the need to consider the apparatus that monitors or observes them. Thus, in classical theories, interference can only occur between waves of the same nature. In quantum theory, the observed results require a description of the system and its measuring apparatus, which allows us to rethink the explanation of various natural phenomena. In this paper, we consider the ion-trap platform to study the interference of waves with different physical natures, specifically the electromagnetic and mechanical. At first, we drive two lasers onto a single-trapped ion to produce Jaynes-Cummings and Carrier interactions, where we verify that, depending on the phase relationship between the coherent state of the vibrational (mechanical) mode and the Carrier pulse (electromagnetic wave), the interactions enhance or cancel out population transfer to the electronic state of the ion, that works out as our measuring apparatus for those waves. Extending our result to an ion chain, we verify that a precise modulation of the Carrier Rabi frequency and phase (electromagnetic pulse) according to the amplitude of the incoming mechanical coherent state in the ion chain enables creating either constructive or destructive interference with propagating pulses, in which the electronic state of the driven ion is, respectively, populated more and faster, or transparent to both pulse waves, when the information flux behaves as if no external fields are applied. Finally, this new type of controlled interference between waves of different natures allows us to propose new hybrid quantum devices, such as transistors or filters of wave packets, where photonic (phononic) pulses control the passage of phononic (photonic) waves.

DOI
10.48550/arxiv.2508.06683

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Classically, wave interference is a phenomenon that can be explained by considering only the waves themselves, that is, without the need to consider the apparatus that monitors or observes them. Thus, in classical theories, interference can only occur between waves of the same nature. In quantum theory, the observed results require a description of the system and its measuring apparatus, which allows us to rethink the explanation of various natural phenomena. In this paper, we consider the ion-trap platform to study the interference of waves with different physical natures, specifically the electromagnetic and mechanical. At first, we drive two lasers onto a single-trapped ion to produce Jaynes-Cummings and Carrier interactions, where we verify that, depending on the phase relationship between the coherent state of the vibrational (mechanical) mode and the Carrier pulse (electromagnetic wave), the interactions enhance or cancel out population transfer to the electronic state of the ion, that works out as our measuring apparatus for those waves. Extending our result to an ion chain, we verify that a precise modulation of the Carrier Rabi frequency and phase (electromagnetic pulse) according to the amplitude of the incoming mechanical coherent state in the ion chain enables creating either constructive or destructive interference with propagating pulses, in which the electronic state of the driven ion is, respectively, populated more and faster, or transparent to both pulse waves, when the information flux behaves as if no external fields are applied. Finally, this new type of controlled interference between waves of different natures allows us to propose new hybrid quantum devices, such as transistors or filters of wave packets, where photonic (phononic) pulses control the passage of phononic (photonic) waves.
Trapped ions are one of the leading platforms for quantum technologies due to their excellent control over their internal electronic and external motional degrees of freedom. Many techniques and interesting effects rely on the coupling of the ions to their motion, which makes precise control of them paramount. In this work, two novel techniques for motional state detection are presented. They allow the probing of certain motional states with a single measurement, without affecting the motion of the measured ion. These techniques are employed to generate and detect a highly entangled state between two motional modes in a novel manner. Furthermore, we harness the rich and intricate dynamics arising from the coupling of the ion's motion to its electronic degrees of freedom to study the emergence of interference. Theoretical predictions, describing interference both in the quantum and the classical regimes, are verified, offering a new and more intuitive description of interference, not just for trapped ions, but for a variety of systems that can be described in a similar way. On the other hand, Rydberg excitation with trapped ions enables new interaction mechanisms and makes them extremely sensitive to their surroundings. This thesis presents advances towards Rydberg experiments with longer ion strings and concludes with a first demonstration of coherent population transfer between Rydberg states in trapped ions. The methods developed significantly increase the toolbox for trapped Rydberg ions, enabling more sophisticated experiments, especially when multiple different Rydberg states are involved, and allow more flexibility when using longer ion strings.
Abstract Quantum interference plays a central role in the realm of quantum particles, revealing their wave‐like nature and probabilistic behavior. It relies on the concept of superposition, where the probability amplitudes of different processes that contribute to the given phenomenon interfere with each other. When combined, their phases can interfere either constructively or destructively. Quantum interference manifests in three distinct forms: optical interference, arising from the interaction of light waves and forming the basis for technologies such as lasers and optical filters; interference via atoms, which involves manipulating atomic states to control light–matter interactions and enables techniques like Stimulated Raman Adiabatic Passage and Electromagnetically Induced Transparency in quantum information processing; and interference of atoms with themselves, in which the matter waves of single atoms interfere with each other, as employed in precision measurements such as atom interferometry–a crucial tool for applications in quantum mechanics and precision navigation. These diverse forms of quantum interference have profound implications for numerous scientific disciplines, demonstrating that interference can involve particles beyond just photons.
Experimental and theoretical work is presented on the control of wave packet dynamics in atomic and molecular systems. Using sequences of phase-locked optical pulses, the link between optical phase and quantum mechanical phase is explored in the Na atom and Naj dimer, representing a step towards the logical engineering of quantum states in more complicated systems. A novel apparatus, constructed to study and control the vibrational dynamics of vibrational wave packets on the Na ionic potential surface, is described in chapter 3. Theoretical simulations for proposed experiment are presented in chapter 4. Control is achieved by exploiting the phase-evolution of the constituent vibrational quantum states within the wave packet superposition. The phase relationship and the accumulated phase difference between the various components of the wave packet is determined, and a sequence of phase-locked optical pulses is employed to selectively enhance or depopulate specific vibrational states, or sets of vibrational states. The quantum state composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multi-pulse response of the time-dependent vibrational state populations. In chapter 5, the quantum interference between Rydberg electron wave packets in the Na atom is investigated using pairs of phase-locked wave packets, allowing manipulation of the total orbital angular momentum of Na Rydberg atoms. Initially the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows specific angular momentum compositions within the resultant wave packet to be engineered. Experimentally, this final quantum state distribution is analysed in the frequency domain using state selective field ionisation, and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets.
The quantum nondemolition measurement is applied to a two-dimensional (2D) trapped-ion model in which two laser beams drive the corresponding vibrational motions and are carrier resonant with the two-level system of the ion. The information about the ionic vibrational energy can be detected by the occupation probability of the internal electronic level. The substantial difference of the 2D model from the one-dimensional one is that two orthogonal beams have a fixed phase shift instead of statistical independence. As a result, the atomic Rabi oscillation is involved in the coherent superposition of two sub-Rabi oscillations induced by the corresponding driving beams. This means that, in the bidimensional case, the phase difference between the two laser beams plays the role of an adjustable external parameter which allows us to optimize the measurement scheme itself, in terms of precision and sensitivity. As in the one-dimensional case, our proposal leads to interesting applications as, for example, the cooling and preparation of arbitrary bimodal Fock states. The model can be considered as a cooling method for the trapped ion from the vibrational thermal state to the vacuum state. Due to the coherent superposition of two sub-Rabi oscillations, the Rabi frequency degeneration and offset may occur in this model. This provides the possibility of generating various entangled superposition of Fock states, the pair coherent state, and entangled pair coherent states.
We have shown that electromagnetically induced transparency can be achieved by control-probe interferometry using two delayed phase-locked ultrashort pulses. Two vibrational wavepackets on the excited state, excited by two delayed phase-locked ultrashort pulses, interfere constructively or destructively leading to enhancement or suppression of absorption to a selective set of vibrational levels. Depending on the phase difference and the delay between the pulses with same carrier frequency, one can design different transparency windows between absorption peaks at consecutive even(odd) vibrational levels by eliminating absorption at odd(even) vibrational levels. We have shown that by switching the phase difference of two delayed femtosecond pulses, one can switch to complete elimination of absorption from enhanced absorption to a particular set of vibrational levels in the excited state. Thus, switching of transparency through window between odd vibrational levels to that between even vibrational levels is possible. By properly choosing the temporal width and the carrier frequency of the pulses, lossless transmission of complete or bands of frequencies of the pulses can be achieved through these transparency windows. Hence, designing of single- or multi-mode transparency windows in NaH molecule is feasible by control-probe quantum interferometry.
A scheme is presented for the generation of macroscopic quantum-interference states for the motion of a trapped ion. In the scheme the ion is driven by a standing-wave laser beam whose carrier frequency is tuned to the ion transition. The distinct feature of the scheme is that the time required to generate the desired state is limited only by the available laser intensity, not by inherent mechanisms such as off-resonant excitations. Therefore, our scheme may allow the generation of the desired state at a high speed, which is important in view of decoherence. In the two-dimension case, entangled coherent states can be obtained. The scheme can also be used to generate entangled states for multiple modes of NNN trapped ions with a single strong standing-wave laser pulse.