High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.
High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.
This perspective introduces attosecond qubits: coherent two-level subsystems that arise naturally in strong-field physics from the interference of experimentally distinguishable quantum pathways. These attosecond qubits are dynamical superposition states formed during strong-field evolution and appear in diverse settings: short-long trajectories in HHG, early-late ionization bursts, polarization-selective recombination channels, and momentum- or energy-bin structures in ATI. Attosecond qubits can be prepared, rotated, and measured using existing attosecond techniques, providing a Hilbert-space description of sub-cycle electronic dynamics. Coulomb interaction, tunneling fluctuations, soft-photon dressing, and macroscopic propagation define ultrafast decoherence channels. This framework links attosecond physics with quantum information science and identifies new opportunities for coherence metrology, temporal quantum tests, ultrafast decoherence studies, and the exploration of quantum speed limits in strongly driven, time-dependent Hamiltonians.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically non-classical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways -- short and long trajectories -- during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schrödinger cat-like states in the driving field. Additionally, using an ab-initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the non-classical characteristics of the emitted light.
The generation and control of extreme ultraviolet (XUV) radiation by high harmonic generation (HHG) have advanced ultrafast science, providing direct insights into electron dynamics on their natural time scale. Attosecond science has established the capability to resolve ultrafast quantum phenomena in matter by characterizing and controlling the classical properties of the high harmonics. Recent theoretical proposals have introduced novel schemes for generating and manipulating XUV HHG with distinct quantum features, paving the way to attosecond quantum optics. In this work, we transfer fundamental concepts in quantum optics into attosecond science. By driving the HHG process with a combination of an infrared bright squeezed vacuum (BSV, a non-classical state of light), and a strong coherent field, we imprint the quantum correlations of the input BSV onto both the ultrafast electron wavefunction and the harmonics' field. Performing in-situ HHG interferometry provides an insight into the underlying sub-cycle dynamics, revealing squeezing in the statistical properties of one of the most fundamental strong-field phenomena -- field induced tunneling. Our measurement allows the reconstruction of the quantum state of the harmonics through homodyne-like tomography, resolving correlated fluctuations in the harmonic field that mirror those of the input BSV. By controlling the delay between the two driving fields, we manipulate the photon statistics of the emitted attosecond pulses with sub-cycle accuracy. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.
Correlations between optical modes, ranging from classical fluctuations to quantum entanglement, are a cornerstone of modern optics and emerging quantum technologies. However, probing these correlations on the natural timescale of electronic motion - the attosecond regime - remains a major challenge. Here, we generate and characterize correlated attosecond extreme-ultraviolet (XUV) emission by perturbing gas-phase high-harmonic generation with two-mode bright squeezed vacuum. The signal and idler fields imprint their correlated amplitude and phase fluctuations onto two families of harmonics, thereby transferring these correlations from the infrared to broadband XUV modes. Even harmonics serve as an intrinsic attosecond phase-sensitive probe of these correlations through interference between indistinguishable XUV pathways. Shot-resolved covariance measurements reveal the amplitude correlations, while even-harmonics resolve the phase correlations with sub-cycle precision. Time-domain reconstruction of the correlated emission reveals a transition from maximal fluctuations to near-silence within only 30 as. Whereas the signal and idler driven attosecond pulse trains exhibit excess fluctuations individually, their joint reconstruction shows strongly suppressed fluctuations, reflecting their shared correlations. These results establish a framework for generating and probing quantum correlations on attosecond timescales, opening the door to quantum attosecond science.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically nonclassical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways, short and long trajectories, during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum-optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schr\"odinger-cat-like states in the driving field. Additionally, using an ab initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the nonclassical characteristics of the emitted light.
High-harmonic generation (HHG) is conventionally understood to produce attosecond pulse trains only when the emitted harmonics are mutually phase-locked, in accordance with the classical theory of mode-locking. Such locking is necessary for pulse synthesis when the harmonic field is in a separable multimode quantum state. This requirement, however, can be circumvented entirely for harmonic combs exhibiting intermodal entanglement. We introduce a novel family of multimode quantum states, termed attoquants: states associated with highly structured pulse trains that are inherently insensitive to relative phases. As a concrete example, we analyse the coherent permanent state, constructed as a completely symmetric superposition of products of coherent states over all permutations of a fixed parameter set. It is shown analytically that its electric-field expectation value is a locked Fourier superposition of the driving-field harmonics, yielding an attosecond pulse train without requiring mode-locking. We further calculate the photon statistics, the Wigner function, and the logarithmic negativity of this state, confirming it to be genuinely nonclassical and entangled. Finally, we offer a phenomenological interpretation for the generation of such entangled states during HHG, as a consequence of multi-atom effects. Since the coherence volume of the driving field greatly exceeds that of its harmonics, a collectively-driven cluster of atoms can radiate the individual harmonics as spatially resolved, but fundamentally indistinguishable sources. This can generate the permutation-symmetric entanglement structure of an attoquant.