Using quantum coherence, entanglement, or squeezing to measure physical quantities below the classical shot-noise (standard-quantum) limit. Platforms: NV-centre diamond magnetometry (spin coherence times T₂ up to ms at room temperature;…
quantum-sensing
NV-centre diamond magnetometry: optically-detected magnetic resonance
NV-centre (nitrogen-vacancy) defect in diamond: a substitutional N adjacent to a C-atom vacancy, in the negative charge state, has a…
Squeezed-vacuum injection: 3-dB shot-noise reduction below SQL in LIGO
Caves 1981 proposal: inject a squeezed-vacuum state at the dark-port of a Michelson-interferometric gravity-wave detector such that the…
QND measurement: [A_obs, H_sys+H_int] = 0 → back-action-evasion
Braginsky 1974 / Caves-Thorne-Drever-Sandberg-Zimmermann 1980 quantum non-demolition (QND) measurement: an observable  whose measurement…
Heisenberg limit: δφ ≥ 1/N vs SQL δφ ≥ 1/√N — ratio √N enhancement
For N-probe interferometric phase estimation the Cramér-Rao bound from the quantum Fisher information F_Q gives δφ ≥ 1/√F_Q. Uncorrelated…
NV DC-magnetometry sensitivity: η_B = ℏ/(g_e μ_B · √(N) · T₂* · √t)
Taylor-Cappellaro-Lukin 2008: the NV-centre shot-noise-limited DC-magnetometry sensitivity per unit measurement-time bandwidth is η_B =…
Squeezed phase noise: δφ_sqz = e^{−r}/√N (Caves 1981)
Caves 1981 squeezed-state Mach-Zehnder phase-estimation: injecting a squeezed-vacuum state with squeezing parameter r (amplitude e^{−r} < 1…
Ramsey interferometry: (π/2)–free-evolution(τ)–(π/2); signal convolution of pulse + evolution
Ramsey separated-oscillatory-field interferometry. Setup: a two-level atom prepared in |g⟩, subjected to (1) a π/2-pulse that creates the…
Wigner quasi-probability distribution: W(x,p) = (1/π)∫⟨x+y|ρ|x−y⟩·e^(−2ipy)dy
Wigner quasi-probability distribution: the phase-space representation of a quantum state. Setup: for a density operator ρ on a mode with…
Squeezed vacuum quadrature variance: (ΔX₁)² = e^(−2r)/4, (ΔX₂)² = e^(2r)/4; polar/Bloch decomp of S(r)
Squeezed-vacuum state construction and variance scaling. Setup: the squeeze operator S(r) = exp[(r/2)(a² − a†²)] acts on the vacuum to…
Ramsey fringe visibility: V(τ) = exp(−τ/T₂); P(τ) = 0.5·(1 + V·cos(ωτ + φ))
Ramsey fringe decoherence envelope. From framework F7, the signal visibility decays exponentially with phase-relaxation time T₂: V(τ) =…
Wigner function of Fock states: W_0 = e^(−2(x²+p²))/π; W_1 = (4(x²+p²)−1)·e^(−2(x²+p²))/π
Wigner function of n-photon Fock states. From framework F8, W_n(x,p) = (−1)^n/π · exp(−2(x²+p²)) · L_n(4(x²+p²)), where L_n is the n-th…
Squeezed variance: (ΔX₁)²·(ΔX₂)² = 1/16 (minimum-uncertainty); Δφ = 1/(√N̄·e^r) sub-SQL
Squeezed-state variance product and phase-sensitivity gain. From framework F9, (ΔX₁)² = e^(−2r)/4 and (ΔX₂)² = e^(2r)/4. Product = 1/16…
OPM (Budker-Romalis 2007)
Budker-Romalis 2007 optically-pumped-magnetometer fT-Hz-half; modern OPM-MEG + biomagnetic medical applications.
NV-center (Jelezko 2002)
F Jelezko-J Wrachtrup 2002 single-NV ESR; modern AFM-NV scanning probe; nanoscale magnetometry + NMR applications.
Clock network (Grotti 2018)
Grotti 2018 + IPGT 2024 transportable optical-clock geodesy; cm-level height-measurement; modern relativistic + dark-matter searches.
Storage-ring EDM
Farley 2004 + JEDI 2017 storage-ring electric-dipole-moment proposals; future-2030s axion + dark-matter direct-detection at storage rings.
LIGO squeezed (2019)
LIGO O3 2019 6dB frequency-dependent squeezing; modern A+ upgrade 9dB; key for sub-shot-noise GW astronomy.
Aberration-corrected EM (2007)
Haider-Krivanek 2007 Cs-corrected STEM 0.5 A resolution; modern PtyChography Tate 2018 < 0.4 A; sub-Angstrom imaging single-atoms.
SQUID (Jaklevic 1964)
R Jaklevic 1964 + Clarke 1976 SQUID-magnetometry; modern modern foundational text + nano-SQUID + 2024 chip-scale-MEG portable brain.
NV centre (Doherty 2013)
M Doherty-Awschalom 2013 NV-diamond review; modern modern foundational + nano-MRI + 2024 NV-magnetometer single-cell-imaging biological.
OAM (Budker-Romalis 2007)
D Budker-M Romalis 2007 optical-atomic-magnetometer; modern modern foundational text + SERF fT/√Hz + 2024 chip-scale MEG-OPM portable.
Squeezed-LIGO (Aasi 2013)
Aasi-LIGO 2013 + 2019 squeezed-light enhancement 30-50%; modern modern foundational text + 2024 frequency-dependent ponderomotive-noise…
Atom interferometer (Kasevich-Chu 1991)
M Kasevich-S Chu 1991 (Chu Nobel 1997) atom-interferometer; modern modern foundational text + LIGO-type + 2024 satellite-CACES gravity GG.
Heisenberg limit (Giovannetti 2004)
V Giovannetti-S Lloyd-L Maccone 2004 Heisenberg-limit; modern modern foundational text + GHZ + N00N states + 2024 phase-estimation atomic.