Freely propagating electrons may serve as quantum probes that can become coherently correlated with other quantum systems, offering access to advanced metrological resources. The researchers propose a setup that coherently couples free electrons in an electron microscope to a trapped-ion quantum processor, enabling non-destructive, quantum-coherent detection and the accumulation of information across multiple electrons. The analysis shows that single electrons can induce resolvable qubit excitations, establishing a platform for practical applications such as quantum-enhanced, dose-efficient electron microscopy.

Trapped-Ion Quantum Computer Interfaces with Free Electrons

The team’s analysis revealed that the passage of even a single electron induced measurable excitation in the trapped-ion qubits, a critical step toward practical quantum-enhanced microscopy. This combination is unusual, as TEMs are traditionally employed for high-resolution materials imaging, not quantum information processing. This approach allows for non-destructive, quantum-coherent detection and the potential to accumulate information from multiple electrons, a capability not previously attainable.

Beyond direct detection, the interface opens possibilities for manipulating the quantum state of the electrons themselves. The trapped-ion quantum computer’s universal state-manipulation capabilities allow for the preparation of advantageous quantum probe states, enhancing the sensitivity of electron microscopy.

This is particularly relevant for low-dose imaging, where minimizing electron beam exposure is important to prevent damage to delicate samples. “By using a trapped-ion quantum computer as a detector, a continuous coherent information transfer from the specimen to the quantum computer, mediated by a single or few electrons, could be possible,” the researchers write. The potential extends beyond conventional imaging techniques. The researchers suggest the platform could be adapted for use with quantum free electron lasers and nanoscale electron accelerators, broadening the scope of coherent state preparation and readout.

A multi-pass setup, where an electron interacts repeatedly with both the sample and the quantum computer, could further reduce the required electron dose. This would allow for even more sensitive and less invasive investigations of materials at the atomic scale.

Coulomb Interaction Enables Electron-Qubit Coupling

The Coulomb interaction between a free electron and a trapped ion’s motion facilitates coherent coupling, enabling a quantum computer to register the electron’s passage. This interaction, detailed in recent work, allows for the detection of single electrons via changes induced in a qubit’s quantum state. The research demonstrates that an electron’s interaction with the ion’s center-of-mass motion effectively transfers information to the trapped-ion quantum computer.

This transfer occurs through the application of laser pulses, which couple the ion’s motion to the qubit states. The team modeled the interaction of a single electron with a single trapped ion, describing the coupling strength using the operator $H^{i} n t$ = -1/|r̂ – R̂|. This equation represents the Coulomb interaction between the electron’s position (r̂) and the ion’s center-of-mass (R̂). Calculations show that the probability of internal transitions within the ion, induced by the electron, is negligible under the experimental conditions.

This simplification allowed the researchers to focus on the interaction between the electron and the ion’s external motion, streamlining the model. The analysis relies on a stroboscopic approximation, neglecting the ion’s time evolution during the brief electron-ion interaction. Calculations reveal that the probability of inducing a bit-flip, changing the qubit from the |0⟩ state to the |1⟩ state, reaches 0.1 to 1 for slow electrons and experimentally achievable parameters.

The maximal coupling strength is achieved when the electron beam is focused on the center of the coherent states. A plot illustrates how this probability varies with the size of the cat state, a specific superposition used to encode the qubit. This sensitivity to the qubit’s initial state helps establish a clear signal from the electron’s interaction.

Extending this principle to a quantum computer with multiple ions arranged in a linear array further amplifies the coupling strength, scaling with the number of ions. This collective enhancement opens possibilities for more sensitive and efficient electron detection. The researchers suggest this approach could facilitate weak or strong measurements without disrupting the electron’s quantum state.

This is a significant step toward integrating a trapped-ion quantum computer into the framework of electron microscopy. “Our approach thus represents a significant step towards an integration of a well-established quantum-computing platform into the powerful and versatile framework of electron microscopy,” the researchers state.

The ability to generate many-electron entanglement, as well as exotic ionic and electronic states in a two-path setup, suggests a pathway toward advanced quantum metrology. This coupling scheme offers a novel means of accumulating information across multiple electrons, potentially leading to dose-efficient imaging techniques.

Resolvable Qubit Excitations from Single Electrons

The ability to induce resolvable qubit excitations with single electrons represents an advance in hybrid quantum systems, allowing for coherent interaction between a free-electron beam and a trapped-ion quantum processor. This coupling, achieved through the intermediary of ionic motion, opens a pathway to accumulate information from multiple electrons without destroying their quantum state, a feat previously unattainable. The strength of this interaction reaches probabilities of 0.1 to 1 for bit-flips in the qubit, given slow electrons and experimentally feasible parameters.

Ions, pre-cooled to their motional and electronic ground state, are the quantum interface, using bichromatic laser pulses to couple the electron’s motion to the ion’s qubit degree of freedom. This approach diverges from traditional electron microscopy, which typically treats quantum correlations involving probing electrons as detrimental, instead harnessing them for quantum-coherent detection.

The ions themselves provide a robust platform for quantum information processing, with demonstrated coherent manipulation and projective readout capabilities in systems containing over fifteen ions. The ability to surpass the standard quantum limit through the accumulation of phase shifts from multiple probe electrons suggests a pathway toward more sensitive and efficient electron detection.

Overcoming Dose Limits in Electron Microscopy

Coupling free electrons to a trapped-ion quantum computer allows for the detection of single electron-induced qubit excitations. By coherently coupling these electrons to a trapped-ion quantum processor, researchers can perform non-destructive, quantum-coherent detection, accumulating information across multiple electrons without inducing significant sample damage. The analysis shows that the center-of-mass degree of freedom of the ion is coupled to the valence electron, using bichromatic laser pulses to manipulate the qubit state.

The team’s work addresses a fundamental limitation in electron microscopy: the trade-off between image resolution and sample integrity. Inelastic scattering processes, inherent in electron-sample interactions, cause structural and chemical modifications, imposing a limit on the tolerable electron dose and, consequently, the achievable signal-to-noise ratio.

Improving imaging under these dose constraints requires strategies that maximize information gained per electron, rather than simply increasing beam intensity. The proposed platform offers a means to achieve this by harnessing quantum correlations involving the probing electrons, moving beyond classical measurement paradigms. The researchers write. This interface also grants access to the full space of quantum measurements through the universal state-manipulation capabilities of the quantum processor, establishing a versatile platform for low-dose, quantum-enhanced electron microscopy.

Spot sizes down to 20 picometers can be reached in scanning electron microscopy, demonstrating the feasibility of focusing the electron to the center of the ionic wavefunction. This precise control allows for weak or strong measurements without decoupling the electron from the resonator, a significant improvement over current multi-pass designs. The ability to coherently prepare and read out electron states could enable more precise control and manipulation of electron beams.

Platform for Quantum-Enhanced Microscopy Applications

The ability to resolve individual qubit excitations using single electrons marks a departure from traditional electron microscopy techniques. Bichromatic laser pulses, specifically red- and blue-detuned transitions, mediate this interaction. This control is important for performing non-destructive, quantum-coherent detection, a process that avoids the structural and chemical modifications often induced by conventional electron microscopy.

👉 More information
🗞 Coupling Free Electrons to a Trapped-Ion Quantum Computer
✍️ Elias Pescoller et al.
🧠 DOI: http://link.aps.org/doi/10.1103/w6t7-9txs

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