Coherent coupling of a trapped electron to a distant superconducting microwave cavity

May combine two claims.

In single MW photon counters based upon three-level systems, only MW fields consisting of one photon can be observed, and these are irreversibly lost after detection.

“In those cases, only MW fields consisting of one (and only one) photon can be observed, and these are irreversibly lost after the detection.”

• cites [12] 2009, Microwave photon detector in circuit QED, Phys. Rev. Lett. sourcePartly supported

  The paper describes irreversible photon absorption as the measurement process (p. 1), supporting the claim that detected photons are lost. But it also proposes counting activated absorbers to determine the number of photons in a Fock state (p. 1), and says enough absorbers could capture and count multiple photons (p. 4). It therefore does not support the claim that only one-photon fields can be observed. (LLM, conf=0.90)

  Experimental — accuracy not yet measured
• cites [13] 2016, Single microwave-photon detector using an artificial [lambda]-type three-level system, Nat. Commun. sourceDisputed

  The Results section (“Demonstration of single microwave-photon detection”; page unavailable) explicitly says the detector responds to multi-photon pulses, although it cannot distinguish them from single-photon pulses. The Results section (“Implementation of a single microwave-photon detector”; page unavailable) says an incident photon is downconverted to a photon at another frequency, rather than simply being irreversibly lost. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

May combine two claims.

The quality factor of a superconducting CPW resonator is reduced by three to four orders of magnitude in the presence of a magnetic field, making it inadequate for storing MW photons.

“However, the quality factor of a superconducting CPW resonator is reduced by three to four orders of magnitude in the presence of a magnetic field.19 This makes it inadequate for storing MW photons.”

• cites [19] 2005, Fabrication and characterization of superconducting circuit QED devices for quantum computation, IEEE Trans. Appl. Supercond. sourcePartly supported

  Section VI (p. 4) reports that the quality factor of superconducting CPW resonators depends on the applied magnetic field, with Al more sensitive than Nb. But the text does not give a three-to-four-order-of-magnitude reduction; the numerical data are in Fig. 6, which our text copy represents only as an image placeholder. The Introduction (p. 1) says high internal Q is important for coupling to a single microwave photon, but does not state that a resonator under a magnetic field is inadequate for photon storage. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

May combine two claims.

The electrodes of the geonium chip define the central conducting strip of a CPW transmission line, where MW photons can exist in either the odd or the even mode.

“The electrodes of the geonium chip define the central conducting strip of a CPW transmission line, 8 where MW photons can exist in either one of the two possible propagation modes, 29 the odd or the even mode, of a CPW line.”

• cites [8] 2011, Theory of the coplanar waveguide Penning trap, New J. Phys. sourceSupported
• cites [29] 1982, Coupled slot line field components, IEEE Trans. Microwave Theory Tech. sourceNot checked — no full text of the source

May combine two claims.

The electron is a linear and reversible quantum microwave transducer, unlike single MW photon counters based upon three-level systems.

“This makes the electron a linear and reversible quantum microwave transducer, unlike single MW photon counters based upon three-level systems 12,13 and similar technologies.”

• cites [12] 2009, Microwave photon detector in circuit QED, Phys. Rev. Lett. sourceSupported
• cites [13] 2016, Single microwave-photon detector using an artificial [lambda]-type three-level system, Nat. Commun. sourceSupported

May combine two claims.

In Penning trap experiments, typical RF resonators have Q ~ 10^4, so the particle's energy is irreversibly dissipated almost instantly and τ = 1/Ω is the resistive cooling time constant.

“In Penning trap experiments such as in Refs.33-35, typical values of the used RF resonators 36 are Q 10 4 .Thus, in those cases, once delivered to the resonator, the particle's energy is irreversibly dissipated almost instantly 37 and s ¼ 1=X is denoted as the “resistive cooling time constant.””

• cites [33] 2008, New measurement of the electron magnetic moment and the fine structure constant, Phys. Rev. Lett. sourceSupported
• cites [34] 2011, g factor of hydrogenlike Si2813+, Phys. Rev. Lett. sourceNot checked — no full text of the source
• cites [35] 2011, Observation of spin flips with a single trapped proton, Phys. Rev. Lett. sourcePartly supported

  On p. 2, the paper reports a resonator quality factor of about 5700 and says the proton cools resistively through its interaction with the tank circuits. On p. 3, it defines a cooling time constant, τ_z, but does not give it as 1/Ω or state that energy delivered to the resonator is irreversibly dissipated almost instantly. Its reported Q values also do not establish a typical value of 10^4 across Penning-trap experiments. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites [36] 2009, The quality factor of a superconducting RF resonator in a magnetic field, Rev. Sci. Instrum. sourceNot checked — no full text of the source
• cites [37] 1995, Cooling methods in ion traps, Phys. Scr. sourcePartly supported

  Section 2, “Resistive cooling” (page not supplied), says ions dissipate energy through currents induced in an external circuit and gives a time constant for energy damping. It does not say that energy delivered to the resonator is dissipated almost instantly or identify the time constant as 1/Ω. The Q value is cited to a different reference in the citing sentence, so it is not assessed against this source. (LLM, conf=0.83)

  Experimental — accuracy not yet measured

May combine two claims.

At such low positions, the electrostatic trapping potential becomes anharmonic, and at 80 mK, the expected relative frequency shifts can be estimated to Δω_p/ω_p ≈ 6×10^-11; such fluctuations of ω_p are negligibly small.

“At such low positions, the electrostatic trapping potential becomes anharmonic, 8 and at 80 mK, the expected relative frequency shifts can be estimated to Dxp xp ' 6 Â 10 À11 .Such fluctuations of x p are negligibly small.”

• cites [8] 2011, Theory of the coplanar waveguide Penning trap, New J. Phys. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

An equivalent system has been implemented with two ions held in two Paul traps at a distance of 40 μm.

“An equivalent system has been implemented with two ions held in two Paul traps at a distance of 40 lm.43”

• cites [43] 2011, Coupled quantized mechanical oscillators, Nature sourcePartly supported

  The paper describes two ions, each confined in a separate trapping well, with the wells 40 μm apart (pp. 1–2). It describes one surface-electrode trap producing those two wells, rather than two distinct Paul traps. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

May combine two claims.

When the quantum state of the exchanged MW signal consists of a large number of photons, the coherence or quantum nature of the state will generally degrade more rapidly than for low photon numbers; a larger number of photons will make the signal increasingly nonmonochromatic, and dispersion of the coupling transmission line will need to be considered.

“When the quantum state of the exchanged MW signal consists of a large number of photons, then the coherence or the “quantum nature” of the state will, in general, degrade more rapidly than for low photon numbers.46 A larger number of photons will make the exchanged MW signal increasingly nonmonochromatic, and in that case, the dispersion of the coupling transmission line will need to be considered”

• cites [46] 2001, Propagation of entangled light pulses through dispersing and absorbing channels, J. Opt. B sourcePartly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

• AssumptionThe authors state this as an assumption: In the discussion, one or a small number of MW photons are assumed.

Probably not a substantial claim: may not pass S3 (load-bearing).

The entanglement of electrons stored in one trap has been proposed for quantum metrology applications, such as the enhancement of the g-factor measurement.

“The entanglement of electrons stored in one trap has been proposed for quantum metrology applications, such as the enhancement of the g-factor measurement.49”

• cites [49] 2010, Towards electron-electron entanglement in Penning traps, Phys. Rev. A sourceSupported

May combine two claims.

The coupling Ω is maximum when the electron and cavity are resonant (ω_cavity = ω_p); when detuned, |Z_cavity| decreases, the coupling strength is reduced, and the two maxima become asymmetric.

“The coupling X is maximum when the electron and the cavity are resonant x cavity ¼ x p .In that case, the impedance of the cavity is Z cavity ð0Þ ¼ R ¼ Q x cavity L. 41 When d 6 ¼ 0; jZ cavity ðdÞj decreases, the coupling strength is reduced, and the two maxima become asymmetric, as shown in Fig. 2(c).”

• cites [41] 2004Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionThe authors state this as an assumption: The cavity, as seen from the trap, has been designed to be resonant with the electron cyclotron frequency.

May combine two claims. The quote only partly states this claim.

At very low positions, Ω/Γ is higher for the odd than for the even mode; the even mode disappears at y0 → 0 due to the vanishing electric field component parallel to the conducting surface.

“At very low positions, X=C is higher for the odd than for the even mode; the latter actually disappears at y 0 !0. This is due to the vanishing electric field component parallel to the conducting surface: E x CPW !0 at y 0 !0.”

May combine two claims.

In the case of resonant coupling, two symmetric peaks appear around the cavity's resonance frequency, and the energy exchange rate between the particle and the resonator is given by the width Ω of the dip between both maxima.

“In the case of resonant coupling, two symmetric peaks appear around the cavity's resonance frequency, x cavity .The energy exchange rate between the particle and the resonator is given by the width X of the dip between both maxima.”

May combine two claims.

The dissipation caused by the walls of the connecting transmission line is linked to the superconductor surface resistivity; at 13.99 GHz, it is negligible compared to the dielectric losses.

“The dissipation caused by the walls of the connecting transmission line is linked to the superconductor surface resistivity: R S 5 4p 2 Á 10 À28 x 2 Ohm (with x given in rad/ s).44 At 13.99 GHz, it is negligible when compared to the dielectric losses.”

• cites [44] 1991, High-Tc superconductor waveguides: Theory and applications, IEEE Trans. Microwave Theory Tech. sourceNot checked — no full text of the source

May combine two claims.

For quartz, the loaded quality factor drops below 10^5 at a distance L_TL ≈ 0.8 cm, while both YAG and sapphire sustain Q > 10^5 at separations above 10 cm.

“From the figure, we observe that, for quartz, the loaded quality factor drops below 10 5 at a distance of L TL ' 0:8 cm, while both YAG and sapphire sustain Q > 10 5 at separations above 10 cm.”

• AssumptionThe authors state this as an assumption: The chip is coupled to a remote CPW superconducting cavity.

May combine two claims.

The effective coupling distance D_eff is inversely proportional to the strength of the electric field at the electron's position, E_CPW(y0), of a 1 V microwave propagating along the CPW; E_CPW(y0) = 1 V / D_eff.

“The “effective coupling distance,” D eff , is inversely proportional to the strength of the electric field at the position of the electron, E CPW ðy 0 Þ, of a 1 V microwave propagating along the CPW.In general, both quantities are related through 32 E CPW ðy 0 Þ ¼ 1 V D eff .”

• cites [32] 2012, Electronic detection of a single particle in a coplanar-waveguide Penning trap, Appl. Phys. B sourceNot checked — no full text of the source

May combine two claims.

The geonium chip confines the magnetic field into the trapping region, which decays rapidly away from it; hence B does not reduce the quality factor of the superconducting cavity.

“The geonium chip confines the magnetic field into the trapping region, which decays rapidly away from it, as shown in Fig. 1(d).Hence, B does not reduce the quality factor of the superconducting cavity.”

May combine two claims.

The trap is enclosed within a rectangular metallic box that acts as a microwave resonator far detuned from ω_p, preventing the electron from emitting cyclotron radiation into free space or into any other modes but those of the trap's CPW line.

“It must be observed that, as sketched in Fig. 2(a), the trap is enclosed within a rectangular metallic box.14 This also acts as a microwave resonator far detuned from x p . 10 Hence, it prevents the electron from emitting cyclotron radiation into free space or into any other modes but those of the trap's CPW line, coupling to the remote MW cavity.”

• cites [14] J. Pinder, “The geonium chip: Engineering a scalable planar Penning trap,” Ph.D. thesis (University of Sussex, 2017).Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [10] 2013, A planar Penning trap with tunable dimensionality of the trapping potential, Int. J. Mass Spectrom. sourceNot checked — no full text of the source

May combine two claims.

The trapped electron might witness a more complex quantum microwave field and further reuse or redistribute it to other devices within a MW quantum network.

“In contrast, the trapped electron might “witness” a more complex quantum microwave field and further reuse or redistribute it to other devices within a MW quantum network.”

May combine two claims.

The electron and the cavity are two coupled quantum harmonic oscillators; this is a linear system where the coupling strength Ω is invariant under a number of photons.

“The electron and the cavity are two coupled quantum harmonic oscillators.This is a linear system, where the coupling strength X is invariant under a number of photons.”

May combine two claims.

The system becomes a quantum circuit and can be excited with one single microwave photon, which then oscillates between both components at the coupling frequency Ω.

“This system becomes a quantum circuit and can be excited with a quantum of current, i.e., one single microwave photon.The photon then oscillates between both components at the coupling frequency X.”

• AssumptionThe authors state this as an assumption: The chip is coupled to a remote CPW superconducting cavity.
• AssumptionThe authors state this as an assumption: Photons arriving at the geonium chip exist in one mode of the CPW shaped by the trap's electrodes.
• AssumptionThe authors state this as an assumption: The cavity, as seen from the trap, has been designed to be resonant with the electron cyclotron frequency.

May combine two claims.

The superconducting CPW microwave cavity is equivalent to a parallel tank circuit, the electron's cyclotron motion acts as a series tank circuit, and their interaction corresponds to coupling in parallel.

“The latter is equivalent to a parallel tank circuit, with inductance L, capacitance C, and losses modeled by the resistance R.Moreover, the electron's cyclotron motion acts as a series tank circuit, with equivalent inductance L e and capacitance C e .32 The electron-cavity interaction corresponds to the coupling in parallel to their equivalent electric circuits, 31 as represented in Fig. 2(b).”

• cites [32] 2012, Electronic detection of a single particle in a coplanar-waveguide Penning trap, Appl. Phys. B sourceNot checked — no full text of the source
• cites [31] 1968, Bolometric technique for the RF spectroscopy of stored ions, Phys. Rev. Lett. sourceNot checked — no full text of the source

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

The interaction of a trapped electron with a radio frequency resonator made of lumped elements was first investigated by Dehmelt and Walls and can be described as the coupling of two equivalent electric circuits.

“The interaction of a trapped electron with a radio frequency (RF) resonator made of lumped elements was first investigated by Dehmelt and Walls.31 This interaction is commonly employed for the electronic detection of the trapped particles and can be described as the coupling of two equivalent electric circuits.31”

• cites [31] 1968, Bolometric technique for the RF spectroscopy of stored ions, Phys. Rev. Lett. sourceNot checked — no full text of the source

May combine two claims.

Thereafter, the electrons are simultaneously dropped for a short period to a very low position around 50 μm, switching on briefly the strong coupling with the MW cavities.

“Thereafter, the electrons are simultaneously dropped for a short period of time to a very low position, around 50 lm, hence switching on briefly the strong coupling with the MW cavities.”

May combine two claims.

In contrast to systems where the atomic species are attached to the CPW microwave cavity, the electron quantum MW transducer and the cavity are two fully independent devices, making increasingly complex network topologies possible.

“Furthermore, in contrast to systems where the atomic species are attached to the CPW microwave cavity, [22][23][24][25][26] our electron quantum MW transducer and the cavity are two fully independent devices.This makes increasingly complex network topologies possible, enabling many applications beyond quantum MW memories.”

• cites [22][23][24][25][26]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The electron's cyclotron oscillator enables the linear mapping of the quantum state of any multi-photon microwave field onto an atomic degree of freedom, while keeping the photons stored within the cyclotron quantum state for periods of the order of a minute.

“The electron's cyclotron oscillator enables the linear mapping of the quantum state of any multi photon microwave field onto an atomic degree of freedom.This is possible while keeping the photons stored within the cyclotron quantum state for periods of the order of a minute. 1”

• cites [1] 1999, Observing the quantum limit of an electron cyclotron: QND measurements of quantum jumps between Fock states, Phys. Rev. Lett. sourceNot checked — no full text of the source

May combine two claims.

For the entanglement scheme, cyclotron oscillators must be prepared in the first excited state, n_p = 1, with both particles at a high y0, initially invisible to the cavities due to vanishing coupling.

“For that, cyclotron oscillators must be prepared in the first excited state, n p ¼ 1, with both particles at a high y 0 , i.e., initially invisible to the cavities, due to the vanishing coupling (Fig. 3).”

• AssumptionThe authors state this as an assumption: The cavity, as seen from the trap, has been designed to be resonant with the electron cyclotron frequency.