The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index; 5 of the 20 sources its claims cite were checked for support.
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
Open accessAbstract
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.
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Claims the paper makes
12 No full text of the sources · 12 No basis given · 7 Own interpretation · 2 Partly supported · 2 Couldn’t confirm · accuracy not yet measured
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Because of our piecewise buildup of the 3 .0135 1 Dirac Hamiltonian of Eq. (2), we can strongly reduce the experimental demands to study Dirac equations in 1 .0135 1 and 2 .0135 1 dimensions [1,13].”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
- Could not verifycites [13] sourceExperimental — accuracy not yet measured
The paper’s discussion on p. 1 concerns measuring bosonic-field quadratures with a probe, and its conclusion on p. 4 concerns reducing measurements needed for that task. Searches for a piecewise Dirac Hamiltonian and for 1+1 or 2+1 dimensional Dirac equations found no passage addressing the claim. (LLM, conf=0.76)
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The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Finally, in as much as massless chiral fermions in condensed matter, we could also produce a 1 .0135 1 axial anomaly [17] by changing Eq. (10) into H .0133 1 .0134 D .0136 c.0027xpx .0135 qEx , where x / .0133 a .0135 a y .0134 is a motional displacement.”
What the sources say
- Could not verifycites [17] H. B. Nielsen and M. Ninomiya, Phys. Lett. 130B , 389 (1983). sourceExperimental — accuracy not yet measured
The cited paper discusses quantized ion motion and motional sidebands (p. 2), but our copy does not address a 1+1 axial anomaly or the proposed Dirac Hamiltonian. Searches for axial anomaly and for the Hamiltonian terms found no passage supporting the claim. (LLM, conf=0.76)
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- Could not verify
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“On the other hand, for a massive particle, d.0027x=dt .0136 .0137 .0027 x ; H D .0138 =i @ .0136 .0255 .0010 .0027 y , d.0027y=dt .0222 0 , and so forth. The produced set of differential equations yields a Zitterbewegung oscillatory solution similar to Eq. (7), with the evident simplification via the replacements of HD by H .0133 1 .0134 D , ~ p by px , and ~ .0011 by .0027 x .”
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In the paper
“After a unitary transformation around the x axis, transforming .0027 y into .0027 z , the 1 .0135 1 Dirac equation stemming from Eq. (2) can be cast into i @ @ j .0009 .0133 1 .0134 i =@t .0136 H .0133 1 .0134 D j .0009 .0133 1 .0134 i with”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“Our setup is now reduced to a simultaneous JC .0135 AJC interaction, .0027xpx , and a Stark-shift term .0027 z acting on two internal levels.”
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- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The basic ingredients to implement the 1D Dirac dynamics of Eq. (10) with a single trapped ion are two independent electronic (internal) states coupled to a onedimensional motional degree of freedom.”
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In the paper
“We present a method of simulating the Dirac equation in 3 .0135 1 dimensions for a free spin1 = 2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables.”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“The associated Schro ¨dinger equation, HD j .0009 i .0136 i @ @ j .0009 i =@t , performs the same dynamics as the Dirac equation in 3 .0135 1 dimensions for a free spin1 = 2 particle, where j .0009 i represents the fourcomponent Dirac bispinor.”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“The notorious analogy between Eqs. (3) and (5) shows that the quantum-relativistic evolution of a spin1 = 2 particle can be fully reproduced in a tabletop ion-trap experiment”
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- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the nonrelativistic limit, mc 2 .0029 pxc , or equivalently .0010 .0029 .0017 ~ .0010 , we may identify the dispersive limit in Eq. (10), and derive the squeezing second-order Hamiltonian”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“yielding the expected Schro ¨dinger Hamiltonian associated with the classical kinetic energy of a free particle.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We show also how to simulate the simplified 1 .0135 1 case, requiring the manipulation of only two internal levels and one motional degree of freedom.”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“We propose also the simulation of the Dirac equation in 1 .0135 1 dimensions, requiring only the control of two internal levels and one motional degree”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · hedged
“We focus now on the 1 .0135 1 -dimensional case, which could be reached by current experiments, keeping most striking results available.”
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- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If we consider a bispinor state with a peaked momentum around p 0 , j .0009 0 i .0136 j a i .0010 exp .0137.0255.0133 p .0255 p 0 .0134 2 = 2 .0027 2 p .0138 , the Zitterbewegung frequency associated with the measurable quantity h ~ r .0133 t .0134i can be estimated as”
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In the paper
“The natural way to detect Klein's paradox, assuming an initial positive-energy internal state j a i ( p 0 .0136 0 ), is via measurement of nonzero population in the negativeenergy component j b i .”
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In the paper
“The sudden raise of the constant potential V .0133j a ih a j .0135 j b ih b j.0134 , at a certain time t .0136 t 0 after an evolution associated with H .0133 1 .0134 D , could simulate this phenomenon.”
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In the paper
“Given the flexibility of trapped-ion systems, we will have access to a wide range of tunable experimental parameters [8], allowing for realistic and measurable ! ZB .0024 0 -10 6 Hz and R ZB .0024 0 -10 3 .0023 A , depending on the initial vibronic states.”
What the sources say
- Not checked — no full text of the sourcecites [8] D. Leibfried et al. , Rev. Mod. Phys. 75 , 281 (2003). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“We study some quantum-relativistic effects, like the Zitterbewegung and the Klein's paradox, in terms of measurable observables.”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · boosted
“In conclusion, we have shown how to simulate the Dirac equation in 3 .0135 1 dimensions for a free spin1 = 2 particle, and quantum-relativistic effects like the Zitterbewegung and Klein's paradox, in a single trapped ion.”
boosteddirectSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · boosted
In the paper
“It can be proved straightforwardly [1] that the time evolution of the position operator ~ r .0136 .0133 x; y; z .0134 in the Heisenberg picture, following d~ r=dt .0136 .0137 ~ r; H D .0138 =i @ , reads”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In this case an e .0255 .0255 e .0135 (electron-positron) pair could be created from V .”
What the sources say
- Not checked — no full text of the sourcecites [16] O. Klein, Z. Phys. 53 , 157 (1929). source
hedgeddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In the second case, the total energy E .0133 1 .0134 V < .0255 mc 2 .0135 V can be larger than mc 2 , as noticed by Klein.”
What the sources say
- Not checked — no full text of the sourcecites [16] O. Klein, Z. Phys. 53 , 157 (1929). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“When V > 2 mc 2 , negativeenergy electrons (components) may swallow V , acquiring positive energy and behaving as ordinary electrons, while leaving a hole in the Dirac sea.”
What the sources say
- Not checked — no full text of the sourcecites [16] O. Klein, Z. Phys. 53 , 157 (1929). source
hedgedconditional- Asserted: passes — The authors put it forward as true.
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- Probably not a substantial claim. 14
- It may state two separate claims as one. 8
- The quote only partly states this claim. 2
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“The number of laser beams could be further reduced by electro-optical modulators to provide red and blue sidebands simultaneously [11,12].”
What the sources say
- Partly supportedcites [11] P. C. Haljan et al. , Phys. Rev. Lett. 94 , 153602 (2005). sourceExperimental — accuracy not yet measured
The experimental setup description (p. 2) reports an electro-optic modulator and simultaneous red and blue sidebands in a two-beam Raman setup. But it says the electro-optic modulator bridges the hyperfine gap, while driving an acousto-optic modulator at two frequencies creates the bichromatic field. It does not state that electro-optic modulators further reduce the number of beams. (LLM, conf=0.86)
- Not checked — no full text of the sourcecites [12] C. A. Sackett et al. , Nature (London) 404 , 256 (2000). source
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“In the relativistic limit, mc 2 .0028 pxc , which includes m .0136 0 , the 1 .0135 1 case reduces to H .0133 1 .0134 D .0136 i @ .0017 ~ .0010 .0027 x .0133 a y x .0255 ax .0134 , which produces Schro ¨dinger cats, as commented above [9,10].”
What the sources say
- Partly supportedcites [9] E. Solano, R. L. de Matos Filho, and N. Zagury, Phys. Rev. Lett. 87 , 060402 (2001). sourceExperimental — accuracy not yet measured
The discussion on pp. 2–3 describes ion interactions that generate superpositions of coherent motional states, including a single-ion odd coherent state. It does not identify the interaction as a 1+1 Dirac Hamiltonian or discuss a relativistic or massless limit; the Hamiltonian formulas in our copy are not decoded, so the stated expression cannot be verified. (LLM, conf=0.84)
- Partly supportedcites [10] E. Solano, G. S. Agarwal, and H. Walther, Phys. Rev. Lett. 90 , 027903 (2003). sourceExperimental — accuracy not yet measured
The cavity-QED discussion (p. 2) says its one-atom interaction generates Schrödinger cat states, including at zero detuning. It does not discuss a relativistic or massless Dirac limit, and the Hamiltonian formulas in our copy are undecoded, so it cannot verify the stated Hamiltonian. (LLM, conf=0.83)
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one. The quote only partly states this claim.
- Partly supported
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For a massless particle, we can show that dx=dt .0136 .0137 x; H .0133 1 .0134 D .0138 =i @ .0136 2 .0017 .0001 ~ .0010 .0027 x and d.0027x=dt .0136 .0137 .0027 x ; H .0133 1 .0134 D .0138 =i @ .0136 0 . In consequence, .0027 x is a constant of motion and the time evolution of the position operator, x .0133 t .0134 .0136 x .0133 0 .0134 .0135 2 .0017 .0001 ~ .0010 .0027 x t , is classical and does”
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Then, position and momentum operators are measured when choosing .0030 .0136 .0255 .0025= 2 and .0030 .0136 0 , respectively.”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one. The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“To apply this technique, it is required a particular initial state of the internal states, so the measurement of h x .0133 t .0134i would have to be done in two parts, one associated with each of the suitably projected states, j.0135 .0030 i and j.0255 .0030 i .”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Similarly, we can estimate from Eq. (7) the Zitterbewegung amplitude associated with h ~ r .0133 t .0134i as”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The required states could be composed by two ground-state hyperfine levels of an earth alkaline atomic ion, e.g., of 25 Mg .0135 by j F .0136 3; mf .0136 .0255 3 i and j F .0136 2; mf .0136 .0255 2 i , j a i and j b i , respectively, as depicted in Fig. 1.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We focus now on the 1 .0135 1 -dimensional case, which could be reached by current experiments, keeping most striking results available.”
hedged- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“Considering the available laser intensities [21], all necessary Raman beams could be derived from a single laser source.”
What the sources say
- Not checked — no full text of the sourcecites [21] A. Friedenauer et al. , Appl. Phys. B 84 , 371 (2006). source
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The predicted values for a real electron, ! ZB .0024 10 21 Hz and R ZB .0024 10 .0255 3 .0023 A , are out of experimental reach, the effect has never been observed, and its existence is even questioned by quantum field theory considerations.”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“This is easily seen if we express the Dirac equation”
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
“in its ''supersymmetric'' representation [1]”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Also stated in: § Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion · plain
In the paper
“The Zitterbewegung is a known quantum-relativistic effect consisting of a helicoidal motion of a free Dirac particle, a natural consequence of the noncommutativity of its velocity operator components, c.0011 i , with i .0136 x , y , z .”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
boosteddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“However, the one-particle solutions of the Dirac equation in relativistic quantum mechanics predict some astonishing effects, like the Zitterbewegung and the Klein's paradox.”
What the sources say
- Not checked — no full text of the sourcecites [1] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992). source
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We have studied the 1 .0135 1 case, where experimental needs are minimal while keeping most striking predictions.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This stems from the fact that the relativistic energy related to H .0133 1 .0134 V may be recast into .0133 pc .0134 2 .0136 .0133 E .0133 1 .0134 V .0255 V .0135 mc 2 .0134.0133 E .0133 1 .0134 V .0255 V .0255 mc 2 .0134 , which is positive when either both factors are positive or negative.”
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In the paper
“A recent proposal for realizing fast measurements of motional quadratures [14] relies on the possibility of measuring the population of an ionic internal level, Pa , at short probemotion interaction times .0028 with high precision [15].”
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We suggest to produce potential V with the required characteristics through a fast and homogeneous Stark shift in both internal levels.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
In the paper
“In 1929, Klein noticed [16] the anomalous behavior of Dirac particles in regions where a high potential energy V exists: H .0133 1 .0134 V .0136 H .0133 1 .0134 D .0135 V 1 2 .”
What the sources say
- Not checked — no full text of the sourcecites [16] O. Klein, Z. Phys. 53 , 157 (1929). source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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?
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In the citing paper
“Recently, the non-relativistic electrons in graphene monolayer were found to obey the massless relativistic dispersion known as the Dirac cone, leading to the realization of analogies to Zitterbewegung and Klein tunneling in low-energy condensed-matter physics and atom optics 4 -19 .”
From Observation of interaction-induced phenomena of relativistic quantum mechanics (2021) · cites this paper as [8]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“that is a signature of the interference of particle and antiparticle states”
From Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung (2024) · cites this paper as [79]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“namely the oscillation of the expected value of the position operator X [32-34, 77-91].”
From Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung (2024) · cites this paper as [79]
The cited source says what the claim attributes to it.
In the citing paper
“Zitterbewegung (ZB) refers to the rapid trembling motion of a free Dirac electron caused by the interference between positive and negative energy state components [1, 2].”
From Photonic analog of Zitterbewegung in binary waveguide arrays (2010) · cites this paper as [2]
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“Contrary to these, there has not achieved any progress in the investigation on the ZB of photons since some preliminary studies have been presented [30].”
From Photon wave function and Zitterbewegung (2009) · cites this paper as [30]
Experimental — accuracy not yet measured
In the citing paper
“This was confirmed by very recent calculations which predicted that the decay times of ZB are of the order of femtoseconds to microseconds depending on the system in question [12, 16, 21].”
From Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulses (2009) · cites this paper as [21]
In the citing paper
“All the recent theoretical work on ZB assumed that initially the electrons are represented by Gaussian wave packets [6, 12, 15, 21, 22, 23, 24, 28, 30].”
From Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulses (2009) · cites this paper as [21]
In the citing paper
“It has been noted in earlier works on atomic gases [1][2][3], trapped ions [4,5], and also in layers of graphene [6,7], that it is indeed possible to study relativistic dynamics for systems which are inherently non-relativistic.”
From Atomic Zitterbewegung (2008) · cites this paper as [5]
In the citing paper
“The phonon degrees of freedom in trapped-ion systems provide a natural platform for addressing spin-boson or fermion-boson-type problems through quantum simulation233637383940.”
From From transistor to trapped-ion computers for quantum chemistry (2014) · cites this paper as [36]
In the citing paper
“As shown in [6, 7], the Dirac Hamiltonian for a free particle, H free D = cσ x ˆ p + mc 2 σ z , can be engineered using a simultaneous blue and red sideband interaction of equal strength with the appropriate relative phase, amplitude and detuning ℏ Ω := mc 2 .”
From Klein tunneling and Dirac potentials in trapped ions (2010) · cites this paper as [6]
In the citing paper
“A quantum simulation of the Dirac equation is a useful playground to analyze different regimes and to verify in a table-top experiment predicted phenomena such as Zitterbewegung [9,10] or the Klein paradox [12,13].”
From Relativistic quantum mechanics with trapped ions (2011) · cites this paper as [9]
In the citing paper
“For linear potentials eφ ( x ) = gx the situation is conceptually equivalent to Landau Zener tunneling [16, 24, 25], as shown in Fig 1(a).”
From Quantum Simulation of the Klein Paradox with Trapped Ions (2011) · cites this paper as [24]
In the citing paper
“For ultra-relativistic particles, the probability for tunneling is given by P tunnel = e -2 π Γ , with Γ = m 2 c 3 / 2 ℏ g .”
From Quantum Simulation of the Klein Paradox with Trapped Ions (2011) · cites this paper as [24]
Citations
Cites
Chiral tunnelling and the Klein paradox in graphene
Katsnelson, M. I., Novoselov, K. S., & Geim, A. K. (2006) · Nature Physics · doi:10.1038/nphys384 · Cited by 3,896
Quantum dynamics of single trapped ions
Leibfried, D., Blatt, R., Monroe, C., & Wineland, D. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.281 · Cited by 2,739
The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal
Nielsen, H. B., & Ninomiya, M. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)91529-0 · Cited by 1,708
Demonstration of a Fundamental Quantum Logic Gate
Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M., & Wineland, D. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4714 · Cited by 1,586
Thaller, B. (1992) · doi:10.1007/978-3-662-02753-0 · Cited by 1,530
Experimental entanglement of four particles
Sackett, C. A., Kielpinski, D., King, B. E., Langer, C., Meyer, V., Myatt, C. J., Rowe, M., Turchette, Q. A., Itano, W. M., Wineland, D. J., et al. (2000) · Nature · doi:10.1038/35005011 · Cited by 1,436
Generation of Nonclassical Motional States of a Trapped Atom
Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M., & Wineland, D. J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.1796 · Cited by 1,135
Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac
Klein, O. (1929) · Zeitschrift f�r Physik · doi:10.1007/bf01339716 · Cited by 1,080
Quantum information and relativity theory
Peres, A., & Terno, D. R. (2004) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.93 · Cited by 738
Sonic Analog of Gravitational Black Holes in Bose-Einstein Condensates
Garay, L. J., Anglin, J. R., Cirac, J. I., & Zoller, P. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.4643 · Cited by 731
Cited by
Sorted by citations
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932
“, Dirac particles (Gerritsma et al., 2010; Lamata et al., 2007) or the Klein paradox (Casanova et al.”
BackgroundMethodInfluentialColloquium : Artificial gauge potentials for neutral atoms
Dalibard, J., Gerbier, F., Juzeliūnas, G., & Öhberg, P. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1523 · Cited by 2,033
Quantum simulations with trapped ions
Blatt, R., & Roos, C. F. (2012) · Nature Physics · doi:10.1038/nphys2252 · Cited by 1,629
Ultrastrong coupling regimes of light-matter interaction
Forn-Díaz, P., Lamata, L., Rico, E., Kono, J., & Solano, E. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.025005 · Cited by 1,146
Self-citationQuantum simulation of the Dirac equation
Gerritsma, R., Kirchmair, G., Zähringer, F., Solano, E., Blatt, R., & Roos, C. F. (2010) · Nature · doi:10.1038/nature08688 · Cited by 725
“The full three-dimensional Dirac equation Hamiltonian can be simulated with lasers coupling to the three vibrational eigenmodes and the internal states of a single trapped ion [8].”
BackgroundMethodInfluentialSelf-citation
Metadata
- Authors
- Lamata, L., León, J., Schätz, T., & Solano, E.
- Affiliations
- Consejo Superior de Investigaciones Científicas (ES)
- Max Planck Institute of Quantum Optics (DE)
- Pontificia Universidad Católica del Perú (PE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-06-22
- Volume
- 98
- Issue
- 25
- Pages
- 253005-253005
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1968873885
- Cited by
- 300
- References
- 24
- Citations by year
- 2026: 2 · 2025: 13 · 2024: 7 · 2023: 4 · 2022: 16 · 2021: 17 · 2020: 16 · 2019: 19 · 2018: 17 · 2017: 20 · 2016: 18 · 2015: 21 · 2014: 21 · 2013: 14 · 2012: 21
- FWCI
- 9.38
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- Dirac equation, trapped ions, quantum simulation, spin-1/2 particles, Zitterbewegung, Klein paradox, relativistic effects
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
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