arXiv:quant-ph/0112084 · Physical Review A

Sympathetic cooling of trapped Cd+ isotopes

B. B. Blinov, Louis Deslauriers, P. Lee, M. J. Madsen, Ryan Miller, Christopher R. Monroe

Published Apr 10, 2002• 97 citations

Abstract

We sympathetically cool a trapped ${}^{112}{\mathrm{Cd}}^{+}$ ion by directly Doppler cooling a ${}^{114}{\mathrm{Cd}}^{+}$ ion in the same trap. This is the first demonstration of optically addressing a single trapped ion being sympathetically cooled by a different species ion. Notably, the experiment uses a single laser source, and does not require strong focusing. This paves the way toward reducing decoherence in an ion trap quantum computer based on ${\mathrm{Cd}}^{+}$ isotopes.

DOI: 10.1103/physreva.65.040304

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Spatial separation of ion clouds between sympathetically laser-cooled Cd + -ion isotopes in a Penning trap

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Microwave-driven same-species sympathetic cooling for trapped ions

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Cooling and heating of the quantum motion of trapped cadmium(+) ions.

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Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma

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Physical Review LettersJul 7, 1986375 citations

High-resolution ultraviolet spectra of sympathetically-laser-cooled Cd+ ions

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Physical Review AJan 1, 199630 citations

arXiv:quant-ph/0112084 · Physical Review A

Sympathetic cooling of trapped Cd+ isotopes

B. B. Blinov, Louis Deslauriers, P. Lee, M. J. Madsen, Ryan Miller, Christopher R. Monroe

Published Apr 10, 2002• 97 citations

arXiv HTML PDF

Abstract

We sympathetically cool a trapped

{}^{112}{\mathrm{Cd}}^{+}

ion by directly Doppler cooling a

{}^{114}{\mathrm{Cd}}^{+}

ion in the same trap. This is the first demonstration of optically addressing a single trapped ion being sympathetically cooled by a different species ion. Notably, the experiment uses a single laser source, and does not require strong focusing. This paves the way toward reducing decoherence in an ion trap quantum computer based on

{\mathrm{Cd}}^{+}

isotopes.

DOI: 10.1103/physreva.65.040304

Related papers

Spatial separation of ion clouds between sympathetically laser-cooled Cd + -ion isotopes in a Penning trap

Hidetsuka Imajo, Kazuhiro Hayasaka, R. Ohmukai +3 more

Natural ${\mathrm{Cd}}^{+}$ ions in a Penning trap are cooled sympathetically below 1 K by a Coulomb interaction with directly laser-cooled ${\mathrm{Be}}^{+}$ ions. Spatial separation of the ${\mathrm{Be}}^{+}$ and ${\mathrm{Cd}}^{+}$ ion clouds due to centrifugal force is observed directly. When the frequency of rotation of the ion clouds is accelerated, the separation between ${\mathrm{Cd}}^{+}$ -ion isotopes (A=110 and 116) can be clearly observed, though their mass difference is very small. The equations of motion for 100 ${\mathrm{Be}}^{+}$ ions and 50 ${\mathrm{Cd}}^{+}$ ions are solved to simulate the experiments, and the result shows the spatial separation between the two ion species. The separation between the ${\mathrm{Cd}}^{+}$ -ion isotopes is investigated by comparing the experimental results with numerical calculations.Natural ${\mathrm{Cd}}^{+}$ ions in a Penning trap are cooled sympathetically below 1 K by a Coulomb interaction with directly laser-cooled ${\mathrm{Be}}^{+}$ ions. Spatial separation of the ${\mathrm{Be}}^{+}$ and ${\mathrm{Cd}}^{+}$ ion clouds due to centrifugal force is observed directly. When the frequency of rotation of the ion clouds is accelerated, the separation between ${\mathrm{Cd}}^{+}$ -ion isotopes (A=110 and 116) can be clearly observed, though their mass difference is very small. The equations of motion for 100 ${\mathrm{Be}}^{+}$ ions and 50 ${\mathrm{Cd}}^{+}$ ions are solved to simulate the experiments, and the result shows the spatial separation between the two ion species. The separation between the ${\mathrm{Cd}}^{+}$ -ion isotopes is investigated by comparing the experimental results with numerical calculations.

Physical Review AFeb 1, 199725 citations

Microwave-driven same-species sympathetic cooling for trapped ions

M. C. Smith, E. Vandrey, A. D. Leu +5 more

Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$ Ca $^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ( $\bar{n}\approx 0.16$ ) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$Ca$^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ($\bar{n}\approx 0.16$) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.

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Sympathetic cooling of mixed-species two-ion crystals for precision spectroscopy

Jannes B. Wübbena, Sana Amairi‐Pyka, Olaf Mandel +1 more

Sympathetic cooling of trapped ions has become an indispensable tool for quantum-information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al ${}^{+}$ with Be ${}^{+}$ , Mg ${}^{+}$ , and Ca ${}^{+}$ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al ${}^{+}$ -Ca ${}^{+}$ crystal for different cooling laser configurations.Sympathetic cooling of trapped ions has become an indispensable tool for quantum-information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al${}^{+}$ with Be${}^{+}$, Mg${}^{+}$, and Ca${}^{+}$ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al${}^{+}$-Ca${}^{+}$ crystal for different cooling laser configurations.

arXiv:1202.2730Physical Review AApr 13, 201299 citations

Cooling and heating of the quantum motion of trapped cadmium(+) ions.

Louis Deslauriers

The quest for a quantum system best satisfying the stringent requirements of a quantum information processor has made tremendous progress in many fields of physics. In the last decade, trapped ions have been established as one of the most promising architectures to accomplish the task. Internal states of an ion which can have extremely long coherence time can be used to store a quantum bit, and therefore allow many gate operations before the coherence is lost. Entanglement between multiple ions can be established via Coulomb interactions mediated by appropriate laser fields. Entangling schemes usually require the ions to be initialized to near their motional ground state. The interaction of fluctuating electric fields with the motional state of the ion leads to heating and thus to decoherence for entanglement generation limiting the fidelity of quantum logic gates. Effective ground state cooling of trapped ion motion and suppression of motional heating are thus crucial to many applications of trapped ions in quantum information science. In this thesis, I describe the implementation and study of several components of a Cadmium-ion-based quantum information processor, with special emphasis on the control and decoherence of trapped ion motion. I first discuss the building and design of various ion traps that were used in this work. I also report on the use of ultrafast laser pulses to photoionize and load cadmium ions in a variety of rf Paul trap geometries. A detailed analysis of the photoionization scheme is presented, along with its dependence on controlled experimental parameters. I then describe the implementation of Raman sideband cooling on a single trapped 111 Cd + ion to the ground state of motion, where a ground state population of 97% was achieved. The efficacy of this cooling technique is discussed with respect to different initial motional state distributions and its sensitivity to the presence of motional heating. I also present an experiment where the motion of a single trapped 112 Cd + ion is sympathetically cooled by directly Doppler cooling a 114 Cd + ion in the same trap. The implications of this result are relevant to the scaling of a trapped ion quantum computer, where the unwanted motion of an ion crystal can be quenched while not affecting the internal states of the qubit ions. (Abstract shortened by UMI.)The quest for a quantum system best satisfying the stringent requirements of a quantum information processor has made tremendous progress in many fields of physics. In the last decade, trapped ions have been established as one of the most promising architectures to accomplish the task. Internal states of an ion which can have extremely long coherence time can be used to store a quantum bit, and therefore allow many gate operations before the coherence is lost. Entanglement between multiple ions can be established via Coulomb interactions mediated by appropriate laser fields. Entangling schemes usually require the ions to be initialized to near their motional ground state. The interaction of fluctuating electric fields with the motional state of the ion leads to heating and thus to decoherence for entanglement generation limiting the fidelity of quantum logic gates. Effective ground state cooling of trapped ion motion and suppression of motional heating are thus crucial to many applications of trapped ions in quantum information science. In this thesis, I describe the implementation and study of several components of a Cadmium-ion-based quantum information processor, with special emphasis on the control and decoherence of trapped ion motion. I first discuss the building and design of various ion traps that were used in this work. I also report on the use of ultrafast laser pulses to photoionize and load cadmium ions in a variety of rf Paul trap geometries. A detailed analysis of the photoionization scheme is presented, along with its dependence on controlled experimental parameters. I then describe the implementation of Raman sideband cooling on a single trapped 111 Cd + ion to the ground state of motion, where a ground state population of 97% was achieved. The efficacy of this cooling technique is discussed with respect to different initial motional state distributions and its sensitivity to the presence of motional heating. I also present an experiment where the motion of a single trapped 112 Cd + ion is sympathetically cooled by directly Doppler cooling a 114 Cd + ion in the same trap. The implications of this result are relevant to the scaling of a trapped ion quantum computer, where the unwanted motion of an ion crystal can be quenched while not affecting the internal states of the qubit ions. (Abstract shortened by UMI.)

Jan 1, 20061 citation

Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma

Daniel J. Larson, Jonas Bergquist, J. J. Bollinger +2 more

Sympathetic cooling of trapped ions has been demonstrated in an experiment where $^{198}\mathrm{Hg}^{+}$ ions were confined in a Penning ion trap with laser-cooled $^{9}\mathrm{Be}^{+}$ ions. $^{198}\mathrm{Hg}^{+}$ temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the $^{9}\mathrm{Be}^{+}$ plasma were observed when the $^{198}\mathrm{Hg}^{+}$ ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.Sympathetic cooling of trapped ions has been demonstrated in an experiment where $^{198}\mathrm{Hg}^{+}$ ions were confined in a Penning ion trap with laser-cooled $^{9}\mathrm{Be}^{+}$ ions. $^{198}\mathrm{Hg}^{+}$ temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the $^{9}\mathrm{Be}^{+}$ plasma were observed when the $^{198}\mathrm{Hg}^{+}$ ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.

Physical Review LettersJul 7, 1986375 citations

High-resolution ultraviolet spectra of sympathetically-laser-cooled Cd+ ions

Hidetsuka Imajo, Kazuhiro Hayasaka, R. Ohmukai +3 more

Cadmium ions ( ${\mathrm{Cd}}^{+}$ ) have been cooled sympathetically below 1 K by means of Coulomb interactions with laser-cooled ${\mathrm{Be}}^{+}$ ions that are trapped simultaneously in a Penning trap. The ultraviolet resonance lines (5 ${\mathit{s}}^{\mathrm{}2}$ ${\mathit{S}}_{1/2}$ \ensuremath{\leftrightarrows}5 ${\mathit{p}}^{\mathrm{}2}$ ${\mathit{P}}_{3/2}$ , \ensuremath{\lambda}=214.5 nm) of the cooled ${\mathrm{Cd}}^{+}$ ions were observed using a frequency-doubled cw dye laser. This radiation is based on efficient frequency doubling in a nonlinear crystal [\ensuremath{\beta}- ${\mathrm{BaB}}_{2}$ ${\mathrm{O}}_{4}$ (BBO)] with an external enhancement cavity. The spectra of the six isotopes (A=110--114, and 116) were obtained using a natural isotope mixture, and the reliability of the measured isotope shifts is discussed. \textcopyright{} 1996 The American Physical Society.Cadmium ions (${\mathrm{Cd}}^{+}$) have been cooled sympathetically below 1 K by means of Coulomb interactions with laser-cooled ${\mathrm{Be}}^{+}$ ions that are trapped simultaneously in a Penning trap. The ultraviolet resonance lines (5${\mathit{s}}^{\mathrm{}2}$${\mathit{S}}_{1/2}$\ensuremath{\leftrightarrows}5${\mathit{p}}^{\mathrm{}2}$${\mathit{P}}_{3/2}$, \ensuremath{\lambda}=214.5 nm) of the cooled ${\mathrm{Cd}}^{+}$ ions were observed using a frequency-doubled cw dye laser. This radiation is based on efficient frequency doubling in a nonlinear crystal [\ensuremath{\beta}-${\mathrm{BaB}}_{2}$${\mathrm{O}}_{4}$ (BBO)] with an external enhancement cavity. The spectra of the six isotopes (A=110--114, and 116) were obtained using a natural isotope mixture, and the reliability of the measured isotope shifts is discussed. \textcopyright{} 1996 The American Physical Society.

Physical Review AJan 1, 199630 citations

We sympathetically cool a trapped

{}^{112}{\mathrm{Cd}}^{+}

ion by directly Doppler cooling a

{}^{114}{\mathrm{Cd}}^{+}

{\mathrm{Cd}}^{+}

isotopes.

Natural

{\mathrm{Cd}}^{+}

ions in a Penning trap are cooled sympathetically below 1 K by a Coulomb interaction with directly laser-cooled

{\mathrm{Be}}^{+}

ions. Spatial separation of the

{\mathrm{Be}}^{+}

and

{\mathrm{Cd}}^{+}

ion clouds due to centrifugal force is observed directly. When the frequency of rotation of the ion clouds is accelerated, the separation between

{\mathrm{Cd}}^{+}

-ion isotopes (A=110 and 116) can be clearly observed, though their mass difference is very small. The equations of motion for 100

{\mathrm{Be}}^{+}

ions and 50

{\mathrm{Cd}}^{+}

ions are solved to simulate the experiments, and the result shows the spatial separation between the two ion species. The separation between the

{\mathrm{Cd}}^{+}

-ion isotopes is investigated by comparing the experimental results with numerical calculations.

^{43}

^+

ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state (

\bar{n}\approx 0.16

) and benchmark an induced error on the data qubit of

1.7(4)\times 10^{-4}

per cooling cycle.

{}^{+}

with Be

{}^{+}

, Mg

{}^{+}

, and Ca

{}^{+}

ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al

{}^{+}

-Ca

{}^{+}

crystal for different cooling laser configurations.

Sympathetic cooling of trapped ions has been demonstrated in an experiment where

^{198}\mathrm{Hg}^{+}

ions were confined in a Penning ion trap with laser-cooled

^{9}\mathrm{Be}^{+}

ions.

^{198}\mathrm{Hg}^{+}

temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the

^{9}\mathrm{Be}^{+}

plasma were observed when the

^{198}\mathrm{Hg}^{+}

ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.

Cadmium ions (

{\mathrm{Cd}}^{+}

) have been cooled sympathetically below 1 K by means of Coulomb interactions with laser-cooled

{\mathrm{Be}}^{+}

ions that are trapped simultaneously in a Penning trap. The ultraviolet resonance lines (5

{\mathit{s}}^{\mathrm{}2}

{\mathit{S}}_{1/2}

\ensuremath{\leftrightarrows}5

{\mathit{p}}^{\mathrm{}2}

{\mathit{P}}_{3/2}

, \ensuremath{\lambda}=214.5 nm) of the cooled

{\mathrm{Cd}}^{+}

ions were observed using a frequency-doubled cw dye laser. This radiation is based on efficient frequency doubling in a nonlinear crystal [\ensuremath{\beta}-

{\mathrm{BaB}}_{2}

{\mathrm{O}}_{4}

(BBO)] with an external enhancement cavity. The spectra of the six isotopes (A=110--114, and 116) were obtained using a natural isotope mixture, and the reliability of the measured isotope shifts is discussed. \textcopyright{} 1996 The American Physical Society.