Fake Atoms: Engineered Quantum Systems

• Fake atoms are engineered systems that replicate discrete energy levels and quantum properties of natural atoms, enabling controlled quantum simulations and experiments.
• They are realized via diverse platforms such as quantum defects, quantum dots, superconducting circuits, and classical analogs, each providing unique tunability and addressability.
• Applications span quantum information processing, nanoscale sensing, and many-body physics, with performance metrics including coherence times and quantized energy spectra.

Fake atoms, also termed artificial atoms, pseudo atoms, or quantum defects in specific subfields, denote engineered quantum or mesoscopic systems that replicate key physical attributes of natural atomic systems, such as discrete energy spectra, quantized spin, and (in some cases) strong isolated coherence. These constructs range from single-impurity quantum defects in solids, nanostructured “quantum dots,” macroscopic superconducting circuits acting as two-level systems, to even classical analogs such as bound mesoscopic sphere pairs. The design, analysis, and manipulation of fake atoms provide a versatile platform for simulating atomic physics, advancing quantum information science, and exploring fundamental many-body and solid-state phenomena.

1. Conceptual Taxonomy and Definitions

The term “fake atom” admits several closely related but operationally distinct realizations:

• Quantum defects: Single atomic-scale defects (vacancies, substitutional dopants, adatoms) in a crystalline host lattice, with electronic and spin levels confined by the local lattice environment. Exemplified by NV⁻ centers in diamond or chalcogen vacancies in 2D TMDs, these defects feature level structures and addressability akin to those of isolated atoms (Hus et al., 2022).
• Nanostructured quantum dots: Zero-dimensional, phase-coherent electronic islands in semiconductors or correlated oxides, supporting discrete shell-quantization and Coulomb blockade. Often termed artificial atoms especially when the energy level spacing or shell structure mimics atomic s/p/d patterns (Mannhart et al., 2016).
• Engineered mesoscopic circuits: Macroscopic superconducting circuits, e.g., flux qubits, that behave as true quantum two-level systems interacting with microwave fields, accurately reproducing phenomena such as resonance fluorescence and strong atom-field coupling (Astafiev et al., 2010).
• Confined vacuum resonances: Surface-engineered vacuum states formed via STM manipulation on metal surfaces, producing quantized, atomically addressable field-emission resonances with adjustable tunability and lifetimes (Rejali et al., 2022).
• Classical analogs: Electrostatics- and magnetostatics-bound macroscopic sphere dimers (e.g., “Humblonium”), analogized to atomic bound states (albeit lacking quantum level structure), with clear “Bohr radius”-like equilibrium scales (Chafin, 2014).
• Model-theoretic/algorithmic pseudo atoms: In phase retrieval and crystallographic algorithms, pseudo-atom models serve as formal constructs reflecting the effect of real-space density modification on isolated atoms, aiding in robust structure solution—distinct from true physical systems (Li et al., 2017).

While all fake atoms share the essential property of discrete, controllable level structures, they differ fundamentally from natural atoms in terms of environment (solid-state lattice vs. free space), tunability, and susceptibility to environmental decoherence.

2. Theoretical Frameworks: Hamiltonians and Level Structures

Fake atoms are governed by Hamiltonians that recapitulate key atomic features, but with system-specific modifications:

Quantum Defects and Solid-State Analogs

A prototypical defect Hamiltonian in zero field:

$H_0 = D S_z^2 + E (S_x^2 - S_y^2)$

where $D$ (zero-field splitting) sets the gap between $m_S=0$ and $m_S=\pm1$, $E$ denotes rhombic splitting, and effective spin $S$ is fixed by the local electronic configuration. Couplings to external fields (Zeeman, hyperfine) and controlled strain or electric fields map directly onto atomic manipulations (Hus et al., 2022).

Quantum Dots in Correlated Materials

Atoms in “fake” form within correlated electron systems are modeled by:

$$\hat{H} = \sum_{i=1}^N \left[ \frac{p_i^2}{2m^*} + V(\mathbf{r}_i) \right] + \sum_{i<j} U(\mathbf{r}_i - \mathbf{r}_j)$$

where $V(\mathbf{r})$ is a tunable confinement potential, and $U$ incorporates strong on-site (Hubbard $U$) and possibly exchange or charge-transfer interactions, embedding the correlated nature of the host (Mannhart et al., 2016). Level quantization follows a particle-in-box paradigm, corrected for many-body effects.

Superconducting Artificial Atoms

Macroscopic loop systems with Josephson junctions are reducible to effective two-level Hamiltonians:

$$H = -\frac{1}{2}\hbar\delta\omega\,\sigma_z - \frac{1}{2}\hbar\Omega\,\sigma_x$$

in the rotating frame, with $\delta\omega$—drive detuning—and $\Omega$—field amplitude—governing Rabi dynamics. These Hamiltonians reproduce textbook atomic resonance fluorescence and extinction phenomena (Astafiev et al., 2010).

Engineered 1D Bound Systems

For bosons in a 1D ring with delta impurity, the many-body Hamiltonian is:

$$H = -\frac{1}{2M}\sum_{i=1}^N \frac{\partial^2}{\partial x_i^2} + c \sum_{i=1}^N\delta(x_i) + g\sum_{1 \le i < j \le N}\delta(x_i - x_j)$$

yielding, within mean-field,

$N_c = \frac{2|c|}{g} + 1$

as the maximum number of bosons forming the bound “artificial atom” state (Brauneis et al., 2022).

3. Fabrication, Control, and Measurement Techniques

Atomic-Scale and Mesoscopic Approaches

• STM Engineering: Scanning tunneling microscopy under UHV enables both the imaging and deterministic manipulation (write/erase) of quantum defects in 2D materials, with dI/dV spectroscopy providing direct measurement of level structure and spin states (Hus et al., 2022).
• Nanofabrication and Lithography: Epitaxial growth, electron-beam lithography, and colloidal synthesis support creation of quantum dot arrays or correlated-material islands with adjustable dimensions and coupling (Mannhart et al., 2016).
• Vacuum State Confinement: STM-based atomic assembly exposes metal surface patches, locally confining field-emission resonances; patch size and STM-tip distance tune energy level spacing and occupation (Rejali et al., 2022).
• Superconducting Circuit Integration: CPW structures fabricated on Si, integrated with superconducting loop qubits (multiple Josephson junctions), enable high-fidelity probing of transmission ($|t|^2$) and resonance fluorescence under controlled cryogenic conditions (Astafiev et al., 2010).

Classical Constructs

Designer dimers (“Humblonium”) are formed by juxtaposing charged, magnetized, and diamagnetic spheres in configurable traps, with binding and stability directly evaluated by electrodynamics (Chafin, 2014).

4. Quantum Properties, Coherence, and Many-Body Phenomena

• Discrete and Addressable Levels: Quantum defects and quantum dots display robust, host-tunable level splitting, often with strong atomic-like optical or hyperfine transitions.
• Coherence and Dephasing: For many fake atom platforms, coherence times ($T_2$) are set by environmental decoherence—phonons, stray charges, substrate coupling—with engineered systems (e.g. NV centers) achieving $T_2 \sim 1$ ms at room temperature (Hus et al., 2022). Lifetime tunability of confined vacuum resonances is achieved via control over coupling to local environments (Rejali et al., 2022).
• Nonlinear Dynamics: Superconducting artificial atoms demonstrate strong single-photon nonlinearity and full resonance fluorescence, including emission of Mollow triplets under strong driving (Astafiev et al., 2010).
• Coulomb Blockade and Correlations: In quantum dots, Coulomb charging energies $E_C$ and strong correlation parameters $r_s$ set the regime (weakly vs. strongly correlated), with emergent Mott insulator, Kondo, or exotic magnetic order depending on dot size and host material (Mannhart et al., 2016).
• Many-Body Bound States: Cold atomic gases in 1D bind up to $N_c=2|c|/g+1$ bosons per impurity, forming “artificial atoms” with internal correlations (Brauneis et al., 2022).

5. Applications in Quantum Information, Sensing, and Technology

Quantum Information Science

• Qubits and Gates: Single-spin defects (NV⁻, zigzag graphene ends, engineered TMD vacancies) act as robust qubits, supporting coherent control, initialization, and gate operations. Engineering of defect pairs enables dipolar-coupled two-qubit gates (Hus et al., 2022).
• Single-Photon Sources: Fake atoms in hBN, TMDs, or quantum dots provide on-demand, optically addressable single-photon emitters with achievable linewidths in the GHz range (Hus et al., 2022).
• Quantum Networks: Frequency-locked artificial atoms (e.g., a QD locked via transmission through an atomic vapor) yield universally-indistinguishable photons and scalable entanglement distribution between solid-state nodes (Akopian et al., 2013).
• Quantum Simulation and Many-Body Engineering: Arrays of artificial atoms in correlated hosts or on surfaces simulate Hubbard models, exotic quantum phases, or atomic-scale logic gates (Mannhart et al., 2016).

Sensing and Metrology

• Nanoscale Sensing: Defect spins serve as nanoscale magnetometers, with sensitivities $<1$ nT/Hz${}^{1/2}$, leveraging their spatial localization and environmental stability (Hus et al., 2022).
• Tunable Lifetime/Occupation: Engineered lifetime and state occupation in vacuum-confined artificial atoms enable studies of open quantum systems, resonant tunneling, and atomic-scale devices exhibiting negative differential resistance (Rejali et al., 2022).

Memory and Classical Devices

• Memristors and Switches: Single-atom movement in TMDs creates atomically-scale, non-volatile memory elements—realizing the ultimate limit of miniaturization (Hus et al., 2022).
• Classical Atom Analogs: Humblonium dimers function as tunable model systems for exploring granular gases and classical “plasma” regimes in laboratory conditions (Chafin, 2014).

6. Limitations, Challenges, and Open Directions

• Environmental Sensitivity: Decoherence from phonons, charge noise, and substrate coupling remains a primary limit, with control over local environments via STM or substrate engineering an active area of development (Hus et al., 2022).
• Homogeneity and Scalability: Natural atomic uniformity is generally lacking in semiconductor artificial atoms and native defects; deterministic writing via STM or lithographic patterning partially addresses this (Akopian et al., 2013, Hus et al., 2022).
• Measurement Limitations: Intrinsic linewidths and residual detuning ($\sigma_\Delta \approx 8$ peV for frequency-locked QDs) set limits for quantum information protocols (Akopian et al., 2013).
• Algorithmic Models: In phase retrieval, the pseudo atom approach yields $R_{\rm Tian}$ as a reliable figure of merit at low data resolution, but depends on the validity of the density-modified isolated-atom approximation (Li et al., 2017).
• Thermal and Gravitational Stability: Classical atom analogs (Humblonium) are only metastable due to charge loss and Earnshaw's theorem constraints, but offer hours-long lifetimes and strong, tunable binding strengths in the appropriate regime (Chafin, 2014).

7. Outlook and Future Prospects

The versatility of fake atoms is driving rapid advances across quantum computation, simulation, and sensing. Key frontiers include deterministic defect engineering in 2D and 3D materials, integration of microwave and optical control, benchmarking of quantum gate fidelities against atomic standards, and the development of programmable artificial-atom lattices in correlated hosts for exploring novel quantum phases. The merging of atomic-physics methods with solid-state and surface science continually broadens the scope, ensuring that “fake atoms” remain an essential locus for both applied and fundamental research on the quantum and classical boundaries of matter (Hus et al., 2022, Astafiev et al., 2010, Rejali et al., 2022, Mannhart et al., 2016, Chafin, 2014, Akopian et al., 2013, Li et al., 2017, Brauneis et al., 2022).