Direct Measurement of Time-Frequency Analogues of Sub-Planck Structures

Abstract

Exploiting the correspondence between Wigner distribution function and a frequency-resolved optical gating (FROG) measurement, we experimentally demonstrate existence of the chessboard-like interference patterns with a time-bandwidth product smaller than that of a transform-limited pulse in the phase space representation of compass states. Using superpositions of four electric pulses as realization of compass states, we have shown via direct measurements that displacements leading to orthogonal states can be smaller than limits set by uncertainty relations. In the experiment we observe an exactly chronocyclic correspondence to the sub-Planck structure in the interference pattern appearing for superposition of two Schödinger-cat-like states in a position-momentum phase space.

5 pages, 5 figures

References in corpus (6)

• Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
• Quantum metrology at the Heisenberg limit with ion traps
• Time-frequency Domain Analogues of Phase Space Sub-Planck Structures
• Sub-Planck scale structures in a vibrating molecule in the presence of decoherence
• Entanglement induced Sub-Planck structures
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Cited by in corpus (6)

• Quantum Hypercube States
• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
• Sub-Planck structures: Analogies between the Heisenberg-Weyl and SU(2) groups
• Superposing compass states for asymptotic isotropic sub-Planck phase-space sensitivity
• Time-frequency metrology with two single-photon states: phase space picture and the Hong-Ou-Mandel interferometer
• Sub-shot-noise sensitivity via superpositions of two deformed kitten states