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Cited by 1,409Quantum optics and atomic interactionsQuantum Information and CryptographyMechanical and Optical Resonators

Measurement of Conditional Phase Shifts for Quantum Logic

Open access
Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H., Kimble, H. J.·1995·Physical Review Letters
DOI 10.1103/physrevlett.75.4710
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Abstract

Measurements of the birefringence of a single atom strongly coupled to a high-finesse optical resonator are reported, with nonlinear phase shifts observed for an intracavity photon number much less than one. A proposal to utilize the measured conditional phase shifts for implementing quantum logic via a quantum-phase gate (QPG) is considered. Within the context of a simple model for the field transformation, the parameters of the "truth table" for the QPG are determined.

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Written from the paper’s full text.

TL;DR

The paper reports measurements of conditional phase shifts in a single cesium atom strongly coupled to a high-finesse optical cavity, observing nonlinear phase shifts at intracavity photon numbers much less than one. It extracts a conditional phase shift of about 16° per intracavity photon and evaluates a proposed quantum-phase gate truth table within a simple model.

Key findings

  • Conditional phase shifts of 16° per intracavity photon were extracted from measurements of probe phase versus pump intensity; pump-probe coupling is visible for \(m_b \sim 0.1\), with a 30% reduction of \(|\phi_a|\) as \(m_b\) goes from 0.1 to 0.3 photons.
  • For the proposed quantum-phase gate truth table, straight-line fits yield \(\phi_{++} = (16 \pm 3)^\circ\) and a cross-polarization term of \((0.3 \pm 2)^\circ \approx 0\); with roles interchanged, \(\phi_{-+} = \phi_b\). For the Fig. 4 data, \(\phi_a \approx (17.5 \pm 1)^\circ\), \(\phi_b \approx (12.5 \pm 1)^\circ\), and \(\Delta \approx (16 \pm 3)^\circ\).
  • The measured conditional phase shift of 16° per photon would generate a CHSH sum of 2.02, slightly above the classical upper limit of 2, indicating entanglement for \(\Delta \neq 0\) but difficult to detect experimentally.
  • The atom-cavity system has critical parameters \(m_0 = 0.02\) photons and \(N_0 = 0.94\) atoms, with cavity finesse \(F = 18{,}000\), cavity length 56 µm, and Gaussian waist 35 µm.

Methods

  • Cavity quantum electrodynamics experiment with a single cesium atom in a high-finesse optical cavity; the atom is prepared by optical pumping to \((6S_{1/2}, F=4, m=4)\) before entering the cavity. Probe and pump beams are independently tunable in frequency, power, and polarization, and output polarization is analyzed with a rotatable half-wave plate, polarizer, and balanced heterodyne detectors.
  • Measurements include the weak-field response for \(N = 1.0 \pm 0.1\) atoms and probe phase shift versus pump intensity for \(N = 0.9\) atoms, with pump (probe) detuning of +20 (+30) MHz from atomic resonance. One-photon phase shifts are extracted from initial linear slopes.
  • Analysis uses a model transformation \(|j\rangle_a |k\rangle_b \mapsto e^{i\phi_{jk}} |j\rangle_a |k\rangle_b\), with conditional dynamics when \(\phi_{00}+\phi_{11} \neq \phi_{01}+\phi_{10}\). In the limit \(\beta \to 0\), the reduced density operator gives \(\phi_a \simeq \phi_a - 2m_b \sin(\Delta/2)\), so \(\Delta\) is determined from the initial slope \(\partial \phi_a / \partial m_b\).

Limitations

  • The paper states that necessary and sufficient testing procedures have not yet been established for directly verifying that a laboratory system can perform quantum logic transformations with sufficient fidelity, and it is not known what level of dissipation can be tolerated.
  • The ansatz transformation is not explicitly verified; dissipation is neglected in Eqs. (1,2), and the experiment operates at large detunings to approximate purely dispersive interactions. The quantum-phase gate is proposed rather than implemented, and its truth table is inferred from coherent-state measurements and a simple model.
  • The predicted CHSH violation is small (2.02 versus the classical limit of 2) and “quite difficult to detect experimentally”; the paper also notes that no rigorous procedure is known to compute a transfer matrix with finite dissipation.

Model-written summary. Check it against the paper before relying on it.

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Crossref · 10.1103/physrevlett.75.4710

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 4 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § Results · p. 3

    With the roles of the (a,b) modes interchanged, phi_BnZr+ approximately b.

    “With the roles of the (a,b) modes interchanged, we can likewise nd that BnZr+ b.”
    Quote in the paperNot a substantial claim
  • Findingown data
    § Introduction · p. 1

    Conditional dynamics at the single-photon level between two frequency-distinct fields in an optical resonator were demonstrated.

    “we report the demonstration of conditional dynamics at the single photon level between two frequency-distinct elds in an optical resonator.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Introduction · p. 1

    The phase shift between circular polarization states is conditioned upon the intensity of a pump beam via a Kerr-type nonlinearity.

    “The phase shift between circular polarization states is conditioned upon the intensity of a pump beam via a Kerr-type nonlinearity”
    Quote in the paperSubstantial claim
  • Findingown data
    § Abstract · p. 1

    Measurements of the birefringence of a single atom strongly coupled to a high-finesse optical resonator show nonlinear phase shifts for intracavity photon number much less than one.

    “Measurements of the birefringence of a single atom strongly coupled to a high- nesse optical resonator are reported, with nonlinear phase shifts observed for intracavity photon number much less than one.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Abstract · p. 1

    Conditional phase shifts of 16 degrees per intracavity photon were extracted from the data.

    “with conditional phase shifts 16 per intracavity photon extracted from our data.”
    Quote in the paperSubstantial claim
  • May combine two claims. 12
  • Classified as probably not a substantial claim. 4

  • May combine two claims.

    Findingown data
    § Results · p. 2

    The pump-probe coupling is manifest for m_b around 0.1, with a 30% reduction of |a| as m_b goes from 0.1 to 0.3 photons.

    “Note that the pumpprobe coupling is manifest for mb 0:1, with a 30% reduction of jaj as mb goes from 0.1 to 0.3 photons.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given
    § Setup · p. 2

    The intracavity saturation photon number is m0 = 0.02 photons, the critical atom number is N0 = 0.94 atoms, and the one-photon tipping angle is 2g+T0 = 15 degrees.

    “photon number m0 = 4 2 =3g 2 + = 0:02 photons, the critical atom number N0 = 2 =g 2 + = 0:94 atoms, and the one-photon tipping angle 2g+ T0 = 15.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Results · p. 3

    Straight-line fits to Fig. 4 yield phi++ = (16 +/- 3) degrees and phi_+BnZr - a = (0.3 +/- 2) degrees approximately 0.

    “The straight-line ts shown in Fig. 4 yield ++ = (16 3) and +BnZr BnZr a = (0:3 2) 0 as anticipated.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Results · p. 3

    For data as in Fig. 4, a approximately (17.5 +/- 1) degrees, b approximately (12.5 +/- 1) degrees, and phi approximately (16 +/- 3) degrees.

    “where for data as in Fig. 4, a (17:51) , b (12:5 1) , and (16 3) .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § Proposal · p. 3

    The dominant nonlinear phase shift is phi++ = phi_+BnZr + phi_BnZr+ + phi approximately a + b + phi, with phi not equal to 0 being the condition for nontrivial dynamics.

    “The dominant nonlinear phase shift should then be ++ = +BnZr + BnZr+ + ++ ' a + b + , with 6= 0 again being the condition for nontrivial dynamics.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Fock states asymptotically connect to the dressed states of the atom-cavity system and are the appropriate eigenstates of the transformation.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § Discussion · p. 3

    Single-photon pulses could be generated by a variety of techniques, and the optical response of the system to pulses with duration long compared to the inverse cavity damping time 1/gamma should closely reproduce the steady-state behavior investigated here.

    “Note that single-photon pulses could be generated for this purpose by a variety of techniques and that the optical response of our system to pulses with duration long compared to the inverse cavity damping time 1= should closely reproduce the steadystate behavior investigated here [10].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [10]

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § Discussion · p. 4

    For the parametrization rho_jk d_jk, violations of the CHSH inequality require both self coherence and mutual coherence for the (a,b) qubits and scale linearly with the damping of coherences in the joint density matrix.

    “For example for the parametrization jkdjk we nd that violations of the CHSH inequality require both self coherence and mutual coherence for the (a; b) qubits and scale linearly with the damping of coherences in the joint density matrix.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductnone given
    § Discussion · p. 3

    The full transformation in Eq. (2) has not been explicitly verified, although the assumptions seem reasonable.

    “Our ansatz (1) on the other hand maybe viewed with some skepticism, for although our assumptions seem reasonable we have not explicitly veri ed the full transformation (2).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § Discussion · p. 3

    The parameter phi has model-independent significance as the strength of the dispersive nonlinear interaction between intracavity fields, quoted in degrees per unit of stored energy.

    “We wish to stress that the parameter has modelindependent signi cance as the strength of the dispersive nonlinear interaction between intracavity elds, quoted in degrees per unit of stored energy.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data
    § Results · p. 3

    These measurements realize a nonlinear optical susceptibility at the single photon level and demonstrate the conditional dynamics necessary for implementing quantum logic.

    “These measurements represent the realization of a nonlinear optical susceptibility at the single photon level and unambiguously demonstrate the conditional dynamics necessary for implementing quantum logic.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Any laboratory quantum gate must exhibit coherence and demonstrably produce entanglement between qubits.

  • May combine two claims.

    Interpretationreasoning
    § Discussion · p. 4

    For the input state (|1_BnZr>_a + |1+>_a) tensor (|1_BnZr>_b + |1+>_b)/2, the sum of expectation values in the appropriate CHSH inequality is 2 sqrt(1 + sin^2(phi/2)); the measured conditional phase shift phi approximately 16 degrees per photon would generate a value of 2.02.

    “we consider the input state (j1 BnZr i a +j1 + i a ) (j1 BnZr i b +j1 + i b )=2, for which the sum of expectation values in the appropriate CHSH inequality is 2 q 1 + sin 2 (=2). Note that 2 corresponds to the classical upper limit, while the measured conditional phase shift 16 per photon would generate a value of 2:02”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [13] source

      Not checked in the free run.

    • The authors state this as an assumption: Fock states asymptotically connect to the dressed states of the atom-cavity system and are the appropriate eigenstates of the transformation.

  • May combine two claims.

    Interpretationreasoning
    § Discussion · p. 4

    The output state (2) shows entanglement between pump and probe fields for phi not equal to 0, so there must exist a CHSH inequality violated by correlation measurements on |out>.

    “As regards the second criterion, we note that the output state (2) clearly shows entanglement between the pump and probe elds for 6= 0. Hence there must exist a Clauser-Horne-Shimony-Holt (CHSH) inequality [11] violated by correlation measurements on j out i.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [11]

      Not checked in the free run.

    • The authors state this as an assumption: Fock states asymptotically connect to the dressed states of the atom-cavity system and are the appropriate eigenstates of the transformation.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given
    § Discussion · p. 3

    Given the ability to generate a |1>_a |1>_b state of arbitrary polarization, it would be straightforward to derive states of mutually orthogonal polarization spanning the four-dimensional qubit Hilbert space and to measure directly the diagonal elements of the SU(4) transfer matrix.

    “Given the ability to generate a j1i a j1i b state of arbitrary polarization, it would then be straightforward to derive states of mutually orthogonal polarization to span the fourdimensional qubit Hilbert space, and hence to measure directly the diagonal elements of the SU(4) transfer matrix (which is a task that cannot be accomplished with only coherent states).”
    Quote in the paperNot a substantial claim
13 of 13

  • The authors state this as an assumption.

    Fock states asymptotically connect to the dressed states of the atom-cavity system and are the appropriate eigenstates of the transformation.

    “which amounts to the physically-motivated assumption that Fock states asymptotically connect to the dressed states of the atom-cavity system and hence are the appropriate eigenstates of the transformation.”

  • The paper relies on this without support.

    Any laboratory quantum gate must exhibit coherence and demonstrably produce entanglement between qubits.

    “However, any laboratory quantum gate must exhibit coherence and demonstrably produce entanglement between qubits.”

  • The paper relies on this without support.

    For the particular optical frequencies used, the relevant atomic states form a three-level system.

    “For the particular optical frequencies used, the relevant atomic states form a three-level system shown in the inset to Fig. 1.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Prototype quantum computers that store and process information on individual atoms have already been demonstrated.

    “Although an Avogadro scale computer that can act on 10 23 bits might seem implausible, prototype quantum computers that store and process information on individual atoms have already been demonstrated 64 -65 , 76 -80 .”

    From Ultimate physical limits to computation (2000) · cites this paper as [64]

  • Recently constructed quantum microcomputers use one quantum degree of freedom for each bit and operate at the Heisenberg limit Δt = π hbar/2ΔE for the time needed to flip a bit.

    “The laws of physics do not require redundancy to perform logical operations: recently constructed quantum microcomputers use one quantum degree of freedom for each bit and operate at the Heisenberg limit ∆ t = π ¯ h/ 2∆ E for the time needed to flip a bit 64 -65 , 76 -80 .”

    From Ultimate physical limits to computation (2000) · cites this paper as [64]

  • Ion traps and optical cavities offer promising experimental approaches, but no quantum algorithm has yet been implemented with those systems.

    “Ion traps and optical cavities offer promising experimental approaches 14,15 , but no quantum algorithm has yet been implemented with those systems.”

    From Experimental realization of a quantum algorithm (1998) · cites this paper as [15]

  • Photons are the optimal qubit carrier for fast, reliable long-distance communication.

    “On the other hand, photons clearly represent the best qubit carrier for fast and reliable communication over long distances [5,6], since fast and internal-state-preserving transportation of atoms or ions seems to be technically intractable.”

    From Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network (1997) · cites this paper as [5]

Cites

Flagged first, then by citations

Research works printed but not linked: 12

  1. P.W. Shor, 1994, Proceedings of the 35th Annual Symposium on FOCS
  2. A. Ekert, 1995, AIP Conf. Proc.
  3. S. Lloyd, 1993, Science, 261, 1569, 10.1126/science.261.5128.1569 · DOI · Paper page
  4. A. Barenco, 1995, Phys. Rev. Lett., 74, 4083, 10.1103/PhysRevLett.74.4083 · DOI
  5. T. Sleator, 1995, Phys. Rev. Lett., 74, 4087, 10.1103/PhysRevLett.74.4087 · DOI · Paper page
  6. D. Deutsch, 1989, Proc. R. Soc. London A, 425, 73, 10.1098/rspa.1989.0099 · DOI · Paper page
  7. D. Deutsch, 1994, Cavity Quantum Electrodynamics
  8. Q.A. Turchette, 1995, Appl. Phys. B, 60, S1
  9. R.J. Thompson, 1992, Phys. Rev. Lett., 68, 1132, 10.1103/PhysRevLett.68.1132 · DOI
  10. S. Lloyd, 1995, Phys. Rev. Lett., 75, 346, 10.1103/PhysRevLett.75.346 · DOI · Paper page
  11. A. Barenco, 1995, Proc. R. Soc. London A, 449, 669, 10.1098/rspa.1995.0066 · DOI
  12. J.F. Clauser, 1969, Phys. Rev. Lett., 23, 880, 10.1103/PhysRevLett.23.880 · DOI · Paper page

Cited by

Sorted by citations

Authors
Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H., & Kimble, H. J.
Affiliations
California Institute of Technology (US)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1995-12-18
Volume
75
Issue
25
Pages
4710-4713
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.75.4710
OpenAlex
W2003992904
Cited by
1,409
References
4
Citations by year
2026: 4 · 2025: 19 · 2024: 15 · 2023: 27 · 2022: 24 · 2021: 31 · 2020: 19 · 2019: 19 · 2018: 12 · 2017: 28 · 2016: 46 · 2015: 51 · 2014: 46 · 2013: 54 · 2012: 47
FWCI
27.77
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Mechanical and Optical Resonators
Keywords
conditional phase shift, quantum logic, quantum phase gate, high-finesse optical resonator, nonlinear phase shift, quantum gates

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