1
|
Abstract
Recent developments in laser spectroscopy of atomic ions stored in electromagnetic traps are reviewed with emphasis on techniques that appear to hold the greatest promise of attaining extremely high resolution. Among these techniques are laser cooling and the use of single, isolated ions as experimental samples. Doppler shifts and other perturbing influences can be largely eliminated. Atomic resonances with line widths of a few parts in 10(11) have been observed at frequencies ranging from the radio frequency to the ultraviolet. Experimental accuracies of one part in 10(18) appear to be attainable.
Collapse
|
2
|
Rosenband T, Hume DB, Schmidt PO, Chou CW, Brusch A, Lorini L, Oskay WH, Drullinger RE, Fortier TM, Stalnaker JE, Diddams SA, Swann WC, Newbury NR, Itano WM, Wineland DJ, Bergquist JC. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science 2008; 319:1808-12. [PMID: 18323415 DOI: 10.1126/science.1154622] [Citation(s) in RCA: 1070] [Impact Index Per Article: 66.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Time has always had a special status in physics because of its fundamental role in specifying the regularities of nature and because of the extraordinary precision with which it can be measured. This precision enables tests of fundamental physics and cosmology, as well as practical applications such as satellite navigation. Recently, a regime of operation for atomic clocks based on optical transitions has become possible, promising even higher performance. We report the frequency ratio of two optical atomic clocks with a fractional uncertainty of 5.2 x 10(-17). The ratio of aluminum and mercury single-ion optical clock frequencies nuAl+/nuHg+ is 1.052871833148990438(55), where the uncertainty comprises a statistical measurement uncertainty of 4.3 x 10(-17), and systematic uncertainties of 1.9 x 10(-17) and 2.3 x 10(-17) in the mercury and aluminum frequency standards, respectively. Repeated measurements during the past year yield a preliminary constraint on the temporal variation of the fine-structure constant alpha of alpha/alpha = (-1.6+/-2.3) x 10(-17)/year.
Collapse
Affiliation(s)
- T Rosenband
- National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
3
|
Rosenband T, Schmidt PO, Hume DB, Itano WM, Fortier TM, Stalnaker JE, Kim K, Diddams SA, Koelemeij JCJ, Bergquist JC, Wineland DJ. Observation of the 1S0-->3P0 clock transition in 27Al+. Phys Rev Lett 2007; 98:220801. [PMID: 17677830 DOI: 10.1103/physrevlett.98.220801] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2007] [Indexed: 05/16/2023]
Abstract
We report, for the first time, laser spectroscopy of the 1S0-->3P0 clock transition in 27Al+. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminum's electronic state to the beryllium's hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency nu=1,121,015,393,207,851(6) Hz. They are also used to measure the lifetime of the metastable clock state tau=20.6+/-1.4 s, the ground state 1S0 g factor gS=-0.000,792,48(14), and the excited state 3P0 g factor gP=-0.001,976,86(21), in units of the Bohr magneton.
Collapse
Affiliation(s)
- T Rosenband
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
4
|
Fortier TM, Ashby N, Bergquist JC, Delaney MJ, Diddams SA, Heavner TP, Hollberg L, Itano WM, Jefferts SR, Kim K, Levi F, Lorini L, Oskay WH, Parker TE, Shirley J, Stalnaker JE. Precision atomic spectroscopy for improved limits on variation of the fine structure constant and local position invariance. Phys Rev Lett 2007; 98:070801. [PMID: 17359009 DOI: 10.1103/physrevlett.98.070801] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2006] [Indexed: 05/14/2023]
Abstract
We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm 199Hg+ optical clock transition to the ground state hyperfine splitting in 133Cs. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of <5.8x10(-6) per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of |alpha/alpha|<1.3x10(-16) yr-1, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and 171Yb+ vs other 133Cs standards yield a coupled constraint of -1.5x10(-15)<alpha/alpha<0.4x10(-15) yr-1 and -2.7x10(-15)<d/dtlnmicroCs/microB<8.6x10(-15) yr-1.
Collapse
Affiliation(s)
- T M Fortier
- P-23 Physics Division MS H803, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
5
|
Oskay WH, Diddams SA, Donley EA, Fortier TM, Heavner TP, Hollberg L, Itano WM, Jefferts SR, Delaney MJ, Kim K, Levi F, Parker TE, Bergquist JC. Single-atom optical clock with high accuracy. Phys Rev Lett 2006; 97:020801. [PMID: 16907426 DOI: 10.1103/physrevlett.97.020801] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2005] [Indexed: 05/11/2023]
Abstract
For the past 50 years, atomic standards based on the frequency of the cesium ground-state hyperfine transition have been the most accurate time pieces in the world. We now report a comparison between the cesium fountain standard NIST-F1, which has been evaluated with an inaccuracy of about 4 x 10(-16), and an optical frequency standard based on an ultraviolet transition in a single, laser-cooled mercury ion for which the fractional systematic frequency uncertainty was below 7.2 x 10(-17). The absolute frequency of the transition was measured versus cesium to be 1,064,721,609,899,144.94 (97) Hz, with a statistically limited total fractional uncertainty of 9.1 x 10(-16) the most accurate absolute measurement of an optical frequency to date.
Collapse
Affiliation(s)
- W H Oskay
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
6
|
Seidelin S, Chiaverini J, Reichle R, Bollinger JJ, Leibfried D, Britton J, Wesenberg JH, Blakestad RB, Epstein RJ, Hume DB, Itano WM, Jost JD, Langer C, Ozeri R, Shiga N, Wineland DJ. Microfabricated surface-electrode ion trap for scalable quantum information processing. Phys Rev Lett 2006; 96:253003. [PMID: 16907302 DOI: 10.1103/physrevlett.96.253003] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2006] [Indexed: 05/11/2023]
Abstract
Individual laser-cooled 24Mg+ ions are confined in a linear Paul trap with a novel geometry where gold electrodes are located in a single plane and the ions are trapped 40 microm above this plane. The relatively simple trap design and fabrication procedure are important for large-scale quantum information processing (QIP) using ions. Measured ion motional frequencies are compared to simulations. Measurements of ion recooling after cooling is temporarily suspended yield a heating rate of approximately 5 motional quanta per millisecond for a trap frequency of 2.83 MHz, sufficiently low to be useful for QIP.
Collapse
Affiliation(s)
- S Seidelin
- Time and Frequency Division, NIST, Boulder, Colorado 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
7
|
Schmidt PO, Rosenband T, Koelemeij JCJ, Hume DB, Itano WM, Bergquist JC, Wineland DJ. Spectroscopy of atomic and molecular ions using quantum logic. ACTA ACUST UNITED AC 2006. [DOI: 10.1063/1.2387937] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
|
8
|
Leibfried D, Knill E, Seidelin S, Britton J, Blakestad RB, Chiaverini J, Hume DB, Itano WM, Jost JD, Langer C, Ozeri R, Reichle R, Wineland DJ. Creation of a six-atom 'Schrödinger cat' state. Nature 2005; 438:639-42. [PMID: 16319885 DOI: 10.1038/nature04251] [Citation(s) in RCA: 152] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2005] [Accepted: 09/20/2005] [Indexed: 11/08/2022]
Abstract
Among the classes of highly entangled states of multiple quantum systems, the so-called 'Schrödinger cat' states are particularly useful. Cat states are equal superpositions of two maximally different quantum states. They are a fundamental resource in fault-tolerant quantum computing and quantum communication, where they can enable protocols such as open-destination teleportation and secret sharing. They play a role in fundamental tests of quantum mechanics and enable improved signal-to-noise ratios in interferometry. Cat states are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. Here we report the creation of cat states of up to six atomic qubits. Each qubit's state space is defined by two hyperfine ground states of a beryllium ion; the cat state corresponds to an entangled equal superposition of all the atoms in one hyperfine state and all atoms in the other hyperfine state. In our experiments, the cat states are prepared in a three-step process, irrespective of the number of entangled atoms. Together with entangled states of a different class created in Innsbruck, this work represents the current state-of-the-art for large entangled states in any qubit system.
Collapse
Affiliation(s)
- D Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
9
|
Langer C, Ozeri R, Jost JD, Chiaverini J, Demarco B, Ben-Kish A, Blakestad RB, Britton J, Hume DB, Itano WM, Leibfried D, Reichle R, Rosenband T, Schaetz T, Schmidt PO, Wineland DJ. Long-lived qubit memory using atomic ions. Phys Rev Lett 2005; 95:060502. [PMID: 16090932 DOI: 10.1103/physrevlett.95.060502] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2005] [Indexed: 05/03/2023]
Abstract
We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a magnetic field B approximately = 0.01194 T. We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with 9Be+. We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.
Collapse
Affiliation(s)
- C Langer
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
10
|
Abstract
We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.
Collapse
Affiliation(s)
- P O Schmidt
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | |
Collapse
|
11
|
Ozeri R, Langer C, Jost JD, DeMarco B, Ben-Kish A, Blakestad BR, Britton J, Chiaverini J, Itano WM, Hume DB, Leibfried D, Rosenband T, Schmidt PO, Wineland DJ. Hyperfine coherence in the presence of spontaneous photon scattering. Phys Rev Lett 2005; 95:030403. [PMID: 16090723 DOI: 10.1103/physrevlett.95.030403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2005] [Indexed: 05/03/2023]
Abstract
The coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.
Collapse
Affiliation(s)
- R Ozeri
- NIST Boulder, Time and Frequency Division, Boulder, CO 80305, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
12
|
Chiaverini J, Britton J, Leibfried D, Knill E, Barrett MD, Blakestad RB, Itano WM, Jost JD, Langer C, Ozeri R, Schaetz T, Wineland DJ. Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System. Science 2005; 308:997-1000. [PMID: 15890877 DOI: 10.1126/science.1110335] [Citation(s) in RCA: 100] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.
Collapse
Affiliation(s)
- J Chiaverini
- National Institute of Standards and Technology, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
13
|
Oskay WH, Itano WM, Bergquist JC. Measurement of the (199)Hg+ 5d9 6s2 (2)D(5/2) electric quadrupole moment and a constraint on the quadrupole shift. Phys Rev Lett 2005; 94:163001. [PMID: 15904220 DOI: 10.1103/physrevlett.94.163001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2004] [Indexed: 05/02/2023]
Abstract
The electric-quadrupole moment of the (199)Hg+ 5d9 6s2 (2)D(5/2) state is measured to be theta(D,5/2) = -2.29(8) x 10(-40) C m2. This value was determined by measuring the frequency of the (199)Hg+ 5d10 6s (2)S(1/2) --> 5d9 6s2 (2)D(5/2) optical clock transition for different applied electric-field gradients. An isolated, mechanically stable optical cavity provides a frequency reference for the measurement. We compare the results with theoretical calculations and discuss the implications for the accuracy of an atomic clock based upon this transition. We now expect that the frequency shift caused by the interaction of the quadrupole moment with stray electric-field gradients will not limit the accuracy of the Hg+ optical clock at the 10(-18) level.
Collapse
Affiliation(s)
- W H Oskay
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | | | | |
Collapse
|
14
|
Schaetz T, Barrett MD, Leibfried D, Britton J, Chiaverini J, Itano WM, Jost JD, Knill E, Langer C, Wineland DJ. Enhanced quantum state detection efficiency through quantum information processing. Phys Rev Lett 2005; 94:010501. [PMID: 15698054 DOI: 10.1103/physrevlett.94.010501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2004] [Indexed: 05/24/2023]
Abstract
We investigate theoretically and experimentally how quantum state-detection efficiency is improved by the use of quantum information processing (QIP). Experimentally, we encode the state of one 9Be(+) ion qubit with one additional ancilla qubit. By measuring both qubits, we reduce the state-detection error in the presence of noise. The deviation from the theoretically allowed reduction is due to infidelities of the QIP operations. Applying this general scheme to more ancilla qubits suggests that error in the individual qubit measurements need not be a limit to scalable quantum computation.
Collapse
Affiliation(s)
- T Schaetz
- National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | | | |
Collapse
|
15
|
Chiaverini J, Leibfried D, Schaetz T, Barrett MD, Blakestad RB, Britton J, Itano WM, Jost JD, Knill E, Langer C, Ozeri R, Wineland DJ. Realization of quantum error correction. Nature 2005; 432:602-5. [PMID: 15577904 DOI: 10.1038/nature03074] [Citation(s) in RCA: 321] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2004] [Accepted: 10/01/2004] [Indexed: 11/08/2022]
Abstract
Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.
Collapse
Affiliation(s)
- J Chiaverini
- Time and Frequency Division, Mathematical and Computational Sciences Division, NIST, Boulder, Colorado 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
16
|
Schaetz T, Barrett MD, Leibfried D, Chiaverini J, Britton J, Itano WM, Jost JD, Langer C, Wineland DJ. Quantum dense coding with atomic qubits. Phys Rev Lett 2004; 93:040505. [PMID: 15323743 DOI: 10.1103/physrevlett.93.040505] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2004] [Indexed: 05/24/2023]
Abstract
We report the implementation of quantum dense coding on individual atomic qubits with the use of two trapped 9Be+ ions. The protocol is implemented with a complete Bell measurement that distinguishes the four operations used to encode two bits of classical information. We measure an average transmission fidelity of 0.85(1) and determine a channel capacity of 1.16(1).
Collapse
Affiliation(s)
- T Schaetz
- Time and Frequency Division, NIST, Boulder, Colorado 80305-3328, USA
| | | | | | | | | | | | | | | | | |
Collapse
|
17
|
Barrett MD, Chiaverini J, Schaetz T, Britton J, Itano WM, Jost JD, Knill E, Langer C, Leibfried D, Ozeri R, Wineland DJ. Deterministic quantum teleportation of atomic qubits. Nature 2004; 429:737-9. [PMID: 15201904 DOI: 10.1038/nature02608] [Citation(s) in RCA: 126] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2004] [Accepted: 05/04/2004] [Indexed: 11/08/2022]
Abstract
Quantum teleportation provides a means to transport quantum information efficiently from one location to another, without the physical transfer of the associated quantum-information carrier. This is achieved by using the non-local correlations of previously distributed, entangled quantum bits (qubits). Teleportation is expected to play an integral role in quantum communication and quantum computation. Previous experimental demonstrations have been implemented with optical systems that used both discrete and continuous variables, and with liquid-state nuclear magnetic resonance. Here we report unconditional teleportation of massive particle qubits using atomic (9Be+) ions confined in a segmented ion trap, which aids individual qubit addressing. We achieve an average fidelity of 78 per cent, which exceeds the fidelity of any protocol that does not use entanglement. This demonstration is also important because it incorporates most of the techniques necessary for scalable quantum information processing in an ion-trap system.
Collapse
Affiliation(s)
- M D Barrett
- Time and Frequency Division, NIST, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
18
|
Leibfried D, Barrett MD, Schaetz T, Britton J, Chiaverini J, Itano WM, Jost JD, Langer C, Wineland DJ. Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States. Science 2004; 304:1476-8. [PMID: 15178794 DOI: 10.1126/science.1097576] [Citation(s) in RCA: 124] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The precision in spectroscopy of any quantum system is fundamentally limited by the Heisenberg uncertainty relation for energy and time. For N systems, this limit requires that they be in a quantum-mechanically entangled state. We describe a scalable method of spectroscopy that can potentially take full advantage of entanglement to reach the Heisenberg limit and has the practical advantage that the spectroscopic information is transferred to states with optimal protection against readout noise. We demonstrate our method experimentally with three beryllium ions. The spectroscopic sensitivity attained is 1.45(2) times as high as that of a perfect experiment with three non-entangled particles.
Collapse
Affiliation(s)
- D Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | |
Collapse
|
19
|
Wineland DJ, Barrett M, Britton J, Chiaverini J, DeMarco B, Itano WM, Jelenković B, Langer C, Leibfried D, Meyer V, Rosenband T, Schätz T. Quantum information processing with trapped ions. Philos Trans A Math Phys Eng Sci 2003; 361:1349-1361. [PMID: 12869312 DOI: 10.1098/rsta.2003.1205] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single-qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.
Collapse
Affiliation(s)
- D J Wineland
- Time and Frequency Division, National Institute of Standards and Technology (NIST), Boulder, CO 80305-3328, USA
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
20
|
Bize S, Diddams SA, Tanaka U, Tanner CE, Oskay WH, Drullinger RE, Parker TE, Heavner TP, Jefferts SR, Hollberg L, Itano WM, Bergquist JC. Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock. Phys Rev Lett 2003; 90:150802. [PMID: 12732024 DOI: 10.1103/physrevlett.90.150802] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2002] [Revised: 02/27/2003] [Indexed: 05/24/2023]
Abstract
Over a two-year duration, we have compared the frequency of the 199Hg+ 5d(10)6s (2)S(1/2)(F=0)<-->5d(9)6s(2) (2)D(5/2)(F=2) electric-quadrupole transition at 282 nm with the frequency of the ground-state hyperfine splitting in neutral 133Cs. These measurements show that any fractional time variation of the ratio nu(Cs)/nu(Hg) between the two frequencies is smaller than +/-7 x 10(-15) yr(-1) (1sigma uncertainty). According to recent atomic structure calculations, this sets an upper limit to a possible fractional time variation of g(Cs)(m(e)/m(p))alpha(6.0) at the same level.
Collapse
Affiliation(s)
- S Bize
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
21
|
Leibfried D, DeMarco B, Meyer V, Lucas D, Barrett M, Britton J, Itano WM, Jelenković B, Langer C, Rosenband T, Wineland DJ. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 2003; 422:412-5. [PMID: 12660778 DOI: 10.1038/nature01492] [Citation(s) in RCA: 189] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2002] [Accepted: 02/07/2003] [Indexed: 11/08/2022]
Abstract
Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.
Collapse
Affiliation(s)
- D Leibfried
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
22
|
Ben-Kish A, DeMarco B, Meyer V, Rowe M, Britton J, Itano WM, Jelenković BM, Langer C, Leibfried D, Rosenband T, Wineland DJ. Experimental demonstration of a technique to generate arbitrary quantum superposition states of a harmonically bound spin-1/2 particle. Phys Rev Lett 2003; 90:037902. [PMID: 12570526 DOI: 10.1103/physrevlett.90.037902] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2002] [Indexed: 05/24/2023]
Abstract
Using a single, harmonically trapped 9Be(+) ion, we experimentally demonstrate a technique for generation of arbitrary states of a two-level particle confined by a harmonic potential. Rather than engineering a single Hamiltonian that evolves the system to a desired final state, we implement a technique that applies a sequence of simple operations to synthesize the state.
Collapse
Affiliation(s)
- A Ben-Kish
- NIST Boulder, Time and Frequency Division, Ion Storage Group, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
23
|
DeMarco B, Ben-Kish A, Leibfried D, Meyer V, Rowe M, Jelenković BM, Itano WM, Britton J, Langer C, Rosenband T, Wineland DJ. Experimental demonstration of a controlled-NOT wave-packet gate. Phys Rev Lett 2002; 89:267901. [PMID: 12484856 DOI: 10.1103/physrevlett.89.267901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2002] [Indexed: 05/24/2023]
Abstract
We report the experimental demonstration of a controlled-NOT (CNOT) quantum logic gate between motional and internal-state qubits of a single ion where, as opposed to previously demonstrated gates, the conditional dynamics depends on the extent of the ion's wave packet. Advantages of this CNOT gate over one demonstrated previously are its immunity from Stark shifts due to off-resonant couplings and the fact that an auxiliary internal level is not required. We characterize the gate logic through measurements of the postgate ion state populations for both logic basis and superposition input states, and we demonstrate the gate coherence via an interferometric measurement.
Collapse
Affiliation(s)
- B DeMarco
- NIST, Time and Frequency Division, Ion Storage Group, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
24
|
Leibfried D, DeMarco B, Meyer V, Rowe M, Ben-Kish A, Britton J, Itano WM, Jelenković B, Langer C, Rosenband T, Wineland DJ. Trapped-ion quantum simulator: experimental application to nonlinear interferometers. Phys Rev Lett 2002; 89:247901. [PMID: 12484980 DOI: 10.1103/physrevlett.89.247901] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2002] [Indexed: 05/24/2023]
Abstract
We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of two nth order nonlinear optical beam splitters comprising an interferometer sensitive to phase shift in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with n, and the simulation demonstrates that the use of nonlinear beam splitters (n=2,3) enhances this sensitivity compared to the standard quantum limit imposed by a linear beam splitter (n=1).
Collapse
Affiliation(s)
- D Leibfried
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
25
|
Diddams SA, Udem T, Bergquist JC, Curtis EA, Drullinger RE, Hollberg L, Itano WM, Lee WD, Oates CW, Vogel KR, Wineland DJ. An optical clock based on a single trapped 199Hg+ ion. Science 2001; 293:825-8. [PMID: 11452082 DOI: 10.1126/science.1061171] [Citation(s) in RCA: 159] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped 199Hg+ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 x 10(-15) is measured in 1 second of averaging-a value substantially better than that of the world's best microwave atomic clocks.
Collapse
Affiliation(s)
- S A Diddams
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA.
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
26
|
Meyer V, Rowe MA, Kielpinski D, Sackett CA, Itano WM, Monroe C, Wineland DJ. Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. Phys Rev Lett 2001; 86:5870-5873. [PMID: 11415382 DOI: 10.1103/physrevlett.86.5870] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2001] [Indexed: 05/23/2023]
Abstract
We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.
Collapse
Affiliation(s)
- V Meyer
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305-3328, USA
| | | | | | | | | | | | | |
Collapse
|
27
|
Udem T, Diddams SA, Vogel KR, Oates CW, Curtis EA, Lee WD, Itano WM, Drullinger RE, Bergquist JC, Hollberg L. Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser. Phys Rev Lett 2001; 86:4996-4999. [PMID: 11384404 DOI: 10.1103/physrevlett.86.4996] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2001] [Indexed: 05/23/2023]
Abstract
The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).
Collapse
Affiliation(s)
- T Udem
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | | | | | | | |
Collapse
|
28
|
Rowe MA, Kielpinski D, Meyer V, Sackett CA, Itano WM, Monroe C, Wineland DJ. Experimental violation of a Bell's inequality with efficient detection. Nature 2001; 409:791-4. [PMID: 11236986 DOI: 10.1038/35057215] [Citation(s) in RCA: 162] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome 'loopholes' that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's 'signal' is 2.25 +/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole.
Collapse
Affiliation(s)
- M A Rowe
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | | | | | | | | | | | | |
Collapse
|
29
|
Abstract
We demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace (DFS) of a pair of trapped 9Be+ ions, we protect the qubit from environment-induced dephasing that limits the storage time of a qubit composed of a single ion. We measured the storage time under ambient conditions and under interaction with an engineered noisy environment and observed that encoding into the DFS increases the storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.
Collapse
Affiliation(s)
- D Kielpinski
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80305, USA.
| | | | | | | | | | | | | |
Collapse
|
30
|
Vogel KR, Diddams SA, Oates CW, Curtis EA, Rafac RJ, Itano WM, Bergquist JC, Fox RW, Lee WD, Wells JS, Hollberg L. Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb. Opt Lett 2001; 26:102-104. [PMID: 18033520 DOI: 10.1364/ol.26.000102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of 2x10(-13) in 5 s , to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the Hg(+) clock transition with an improvement in accuracy of ~10(5) compared with its best previous measurement.
Collapse
|
31
|
Sullivan DB, Bergquist JC, Bollinger JJ, Drullinger RE, Itano WM, Jefferts SR, Lee WD, Meekhof D, Parker TE, Walls FL, Wineland DJ. Primary Atomic Frequency Standards at NIST. J Res Natl Inst Stand Technol 2001; 106:47-63. [PMID: 27500017 PMCID: PMC4865291 DOI: 10.6028/jres.106.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The development of atomic frequency standards at NIST is discussed and three of the key frequency-standard technologies of the current era are described. For each of these technologies, the most recent NIST implementation of the particular type of standard is described in greater detail. The best relative standard uncertainty achieved to date for a NIST frequency standard is 1.5×10(-15). The uncertainties of the most recent NIST standards are displayed relative to the uncertainties of atomic frequency standards of several other countries.
Collapse
Affiliation(s)
- D. B. Sullivan
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - J. C. Bergquist
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - J. J. Bollinger
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - R. E. Drullinger
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - W. M. Itano
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - S. R. Jefferts
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - W. D. Lee
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - D. Meekhof
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - T. E. Parker
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - F. L. Walls
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| | - D. J. Wineland
- National Institute of Standards and Technology, Boulder, CO 80305-3328
| |
Collapse
|
32
|
Rafac RJ, Young BC, Beall JA, Itano WM, Wineland DJ, Bergquist JC. Sub-dekahertz ultraviolet spectroscopy of 199Hg+. Phys Rev Lett 2000; 85:2462-2465. [PMID: 10978082 DOI: 10.1103/physrevlett.85.2462] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2000] [Indexed: 05/23/2023]
Abstract
Using a laser that is frequency locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d(10)6s (2)S(1/2)(F = 0)<-->5d(9)6s(2) (2)D(5/2)(F = 2) Deltam(F) = 0 electric-quadrupole transition of a single laser-cooled 199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm ( 1.06x10(15) Hz), yielding a line Q approximately 1.6x10(14). We perform a preliminary measurement of the 5d(9)6s(2) (2)D(5/2) electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.
Collapse
Affiliation(s)
- RJ Rafac
- National Institute of Standards and Technology, Boulder, Colorado 80303, USA
| | | | | | | | | | | |
Collapse
|
33
|
Mitchell TB, Bollinger JJ, Dubin DHE, Huang X, Itano WM, Baughman RH. Direct observations of structural phase transitions in planar crystallized ion plasmas. Science 1998; 282:1290-3. [PMID: 9812887 DOI: 10.1126/science.282.5392.1290] [Citation(s) in RCA: 158] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Laser-cooled 9Be+ ions confined in two-dimensionally extended lattice planes were directly observed, and the images were used to characterize the structural phases of the ions. Five different stable crystalline phases were observed, and the energetically favored structure could be sensitively tuned by changing the areal density of the confined ions. The experimental results are in good agreement with theoretical predictions for the planar (infinite in two dimensions) one-component plasma. Qualitatively similar structural phase transitions occur, or are predicted to occur, in other experimentally realizable planar systems.
Collapse
Affiliation(s)
- TB Mitchell
- T. B. Mitchell, J. J. Bollinger, X.-P. Huang, W. M. Itano, Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80303, USA. D. H. E. Dubin, Department of Physics, University of California at San Diego, La Joll
| | | | | | | | | | | |
Collapse
|
34
|
Wineland DJ, Monroe C, Itano WM, Leibfried D, King BE, Meekhof DM. Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions. J Res Natl Inst Stand Technol 1998; 103:259-328. [PMID: 28009379 PMCID: PMC4898965 DOI: 10.6028/jres.103.019] [Citation(s) in RCA: 276] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/04/1998] [Indexed: 05/02/2023]
Abstract
Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trappedion quantum computation by J. I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.
Collapse
Affiliation(s)
- D J Wineland
- National Institute of Standards and Technology, Boulder, CO 80303
| | - C Monroe
- National Institute of Standards and Technology, Boulder, CO 80303
| | - W M Itano
- National Institute of Standards and Technology, Boulder, CO 80303
| | - D Leibfried
- National Institute of Standards and Technology, Boulder, CO 80303
| | - B E King
- National Institute of Standards and Technology, Boulder, CO 80303
| | - D M Meekhof
- National Institute of Standards and Technology, Boulder, CO 80303
| |
Collapse
|
35
|
Abstract
Single crystals of a one-component plasma were observed by optical Bragg diffraction. The plasmas contained 10(5) to 10(6) single-positive beryllium-9 ions (9Be+) at particle densities of 10(8) to 10(9) per cubic centimeter. In approximately spherical plasmas, single body-centered cubic (bcc) crystals or, in some cases, two or more bcc crystals having fixed orientations with respect to each other were observed. In some oblate plasmas, a mixture of bcc and face-centered cubic ordering was seen. Knowledge of the properties of one-component plasma crystals is required for models of white dwarfs and neutron stars, which are believed to contain matter in that form.
Collapse
Affiliation(s)
- WM Itano
- Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80303, USA
| | | | | | | | | | | |
Collapse
|
36
|
Wineland DJ, Monroe C, Meekhof DM, King BE, Leibfried D, Itano WM, Bergquist JC, Berkeland D, Bollinger JJ, Miller J. Quantum state manipulation of trapped atomic ions. Proc Math Phys Eng Sci 1998. [DOI: 10.1098/rspa.1998.0168] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- D. J. Wineland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - C. Monroe
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. M. Meekhof
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - B. E. King
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Leibfried
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - W. M. Itano
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. C. Bergquist
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Berkeland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. J. Bollinger
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. Miller
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| |
Collapse
|
37
|
Affiliation(s)
- C. Monroe
- National Institute of Standards and Technology, Boulder, Colorado 80303
| | - D. M. Meekhof
- National Institute of Standards and Technology, Boulder, Colorado 80303
| | - B. E. King
- National Institute of Standards and Technology, Boulder, Colorado 80303
| | - D. Leibfried
- National Institute of Standards and Technology, Boulder, Colorado 80303
| | - W. M. Itano
- National Institute of Standards and Technology, Boulder, Colorado 80303
| | - D. J. Wineland
- National Institute of Standards and Technology, Boulder, Colorado 80303
| |
Collapse
|
38
|
Bollinger JJ, Itano WM, Wineland DJ, Heinzen DJ. Optimal frequency measurements with maximally correlated states. Phys Rev A 1996; 54:R4649-R4652. [PMID: 9914139 DOI: 10.1103/physreva.54.r4649] [Citation(s) in RCA: 857] [Impact Index Per Article: 30.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
39
|
Monroe C, Meekhof DM, Leibfried D, King BE, Itano WM, Wineland DJ. Single-Atom Quantum Logic Gate and “Schrödinger Cat” State. ACTA ACUST UNITED AC 1996. [DOI: 10.1364/opn.7.12.0013_1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
40
|
Leibfried D, Meekhof DM, King BE, Monroe C, Itano WM, Wineland DJ. Experimental Determination of the Motional Quantum State of a Trapped Atom. Phys Rev Lett 1996; 77:4281-4285. [PMID: 10062500 DOI: 10.1103/physrevlett.77.4281] [Citation(s) in RCA: 119] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
41
|
Meekhof DM, Monroe C, King BE, Itano WM, Wineland DJ. Generation of nonclassical motional states of a trapped atom. Phys Rev Lett 1996; 76:1796-1799. [PMID: 10060523 DOI: 10.1103/physrevlett.76.1796] [Citation(s) in RCA: 161] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
42
|
|
43
|
Monroe C, Meekhof DM, King BE, Jefferts SR, Itano WM, Wineland DJ, Gould P. Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy. Phys Rev Lett 1995; 75:4011-4014. [PMID: 10059792 DOI: 10.1103/physrevlett.75.4011] [Citation(s) in RCA: 139] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
44
|
Itano WM, Bergquist JC, Bollinger JJ, Gilligan JM, Heinzen DJ, Moore FL, Raizen MG, Wineland DJ. Erratum: Quantum projection noise: Population fluctuations in two-level systems. Phys Rev A 1995; 51:1717. [PMID: 9920631 DOI: 10.1103/physreva.51.1717] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
|
45
|
Wineland DJ, Bollinger JJ, Itano WM, Heinzen DJ. Squeezed atomic states and projection noise in spectroscopy. Phys Rev A 1994; 50:67-88. [PMID: 9910869 DOI: 10.1103/physreva.50.67] [Citation(s) in RCA: 167] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
46
|
Bollinger JJ, Heinzen DJ, Moore FL, Itano WM, Wineland DJ, Dubin DH. Electrostatic modes of ion-trap plasmas. Phys Rev A 1993; 48:525-545. [PMID: 9909626 DOI: 10.1103/physreva.48.525] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
47
|
Itano WM, Bergquist JC, Bollinger JJ, Gilligan JM, Heinzen DJ, Moore FL, Raizen MG, Wineland DJ. Quantum projection noise: Population fluctuations in two-level systems. Phys Rev A 1993; 47:3554-3570. [PMID: 9909363 DOI: 10.1103/physreva.47.3554] [Citation(s) in RCA: 131] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
48
|
Eichmann U, Bergquist JC, Bollinger JJ, Gilligan JM, Itano WM, Wineland DJ, Raizen MG. Young's interference experiment with light scattered from two atoms. Phys Rev Lett 1993; 70:2359-2362. [PMID: 10053542 DOI: 10.1103/physrevlett.70.2359] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
49
|
Wineland DJ, Bollinger JJ, Itano WM, Moore FL, Heinzen DJ. Spin squeezing and reduced quantum noise in spectroscopy. Phys Rev A 1992; 46:R6797-R6800. [PMID: 9908086 DOI: 10.1103/physreva.46.r6797] [Citation(s) in RCA: 740] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
50
|
|