T. M. Graham, E. Oh, and M. Saffman, "Multiscale architecture for fast optical addressing and control of large-scale qubit arrays," Appl. Opt. 62, 3242-3251 (2023)
This paper presents a technique for rapid site-selective control of the
quantum state of particles in a large array using the combination of a
fast deflector (e.g., an acousto-optic deflector) and a
relatively slow spatial light modulator (SLM). The use of SLMs for
site-selective quantum state manipulation has been limited due to slow
transition times that prevent rapid, consecutive quantum gates. By
partitioning the SLM into multiple segments and using a fast deflector
to transition between them, it is possible to substantially reduce the
average time increment between scanner transitions by increasing the
number of gates that can be performed for a single SLM full-frame
setting. We analyzed the performance of this device in two different
configurations: In configuration 1, each SLM segment addresses the
full qubit array; in configuration 2, each SLM segment addresses a
subarray and an additional fast deflector positions that subarray with
respect to the full qubit array. With these hybrid scanners, we
calculated qubit addressing rates that are tens to hundreds of times
faster than using an SLM alone.
Numerical data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Cited By
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
If AOD B is not used to correct the k-vector shift imparted by AOD A, then the beam position will be displaced on the high NA Lens, as shown in Fig. 1. The maximum displacement ${D_{{\rm max}}}$ will depend on the number of SLM partitions, the ratio of the SLM partition size to the beam waist ${q_{{\rm SLM}}}$, and the waist of the beam at the high NA lens ${w_{{\rm lens}}}$ [see Eq. (1)]. The waist ${w_{{\rm lens}}}$ is constrained by the target waist size at the atoms ${w_{\rm a}}$, the focal length of the high NA lens, and the wavelength of the light. We calculated ${D_{{\rm max}}}$ for a number of configurations where the wavelength is 459 nm, the focal length of the high NA lens is ${23}\;{\rm mm}$, and ${q_{{\rm SLM}}} = 5$. For this configuration, we observed that AOD B is needed to avoid beam clipping and coma even for a small number of SLM partitions and moderate ${w_{\rm a}}$. Note that a lens with $NA = 0.7$ and the given focal length has a diameter of 45 mm.
Table 2.
Examples of SLM, AOD, and Beam Size Settings for Configuration 1a
Configuration 1 Addressing Examples
Qubit Array
SLM Partitions
Average Transition Rate
Burst Transition Rate
52
39
181
70
22
190
180
4
198
For each example, the following quantities are listed in columns left to right: the total qubit array size ${N_q} \times {N_q}$, number of partitions into which the SLM is divided, the ratio of the beam waist in AOD A (see Fig. 3) to the AOD crystal length (${q_{{\rm AOD,A}}}$), the average transition rate between different addressing patterns, and the burst rate between SLM resets. Each setting is consistent with a $1000 \times 1000$ pixel SLM, 2D AODs with $11.5\;{\unicode{x00B5} \rm s}$ transition time and time-bandwidth product of $TBW = 575$, SLM patch size to beam waist on the SLM ratio of ${q_{{\rm SLM}}} = 5$, and array spacing to beam waist ratio of ${q_a} = 3$.
Table 3.
Examples of SLM and Beam Size Settings for Configuration 2a
Configuration 2 Addressing Examples
Array Size
SLM Partitions
Subarray Size
Transition Rate
2
90
30
650
3
45
15
325
4
27
9
195
2
72
20
416
30
8
173
30
3.6
78
For each example, the following quantities are listed in columns left to right: the total qubit array size, number of partitions into which the SLM is divided, the dimensions of the subarray that each SLM patch addresses, the maximum simultaneous addressing number ${k_{{\rm max}}}$ for which ${P_{{\rm tot}}}$ [see Eq. (17)] is less than or equal to the number of SLM partitions, the ratio of the beam waist in AOD A (see Fig. 1) to the AOD active aperture length (${q_{{\rm AOD,A}}}$), the ratio of beam waist in AOD C to the active aperture length (${q_{{\rm AOD,C}}}$), and the average transition rate between different addressing patterns. Note that in the last two rows ${k_{{\rm max}}}$ is 2, but more than half of the three beam combinations could be included in the SLM partitions. Each of these settings is consistent with a $1000 \times 1000$ pixel SLM, 2D AODs with 11.5 µs transition time, $TBW = 575$, SLM patch size to beam waist on the SLM ratio ${q_{{\rm SLM}}} = 5$, and an array spacing to beam waist ratio of ${q_{\rm a}} = 3$.
Table 4.
SLM Patterns for Different Qubit Addressing Patterns in Configuration 2a
Configuration 2 SLM Partitions
Addressed Qubit Sub-Region
Simultaneously Addressed Sites
Unique Configurations
2
13
3
61
4
158
2
25
3
229
2
41
3
621
In configuration 2, the diffracted pattern from the SLM can be translated with respect to the array using AOD C. With this degree of freedom, the SLM only must address a subregion to address the full qubit array. The number of SLM patches needed for arbitrary addressing of this subregion depends on the dimensions of the subregion (${m_s} \times {n_s}$) and the maximum number of qubit sites to be simultaneously addressed (${k_{{\rm max}}}$). The total number of SLM patches needed to arbitrarily address any combination of sites up to ${k_{{\rm max}}}$ sites simultaneously in the subregion is then equal to ${P_{{\rm tot}}}({m_s},{n_s},{k_{{\rm max}}})$.
If AOD B is not used to correct the k-vector shift imparted by AOD A, then the beam position will be displaced on the high NA Lens, as shown in Fig. 1. The maximum displacement ${D_{{\rm max}}}$ will depend on the number of SLM partitions, the ratio of the SLM partition size to the beam waist ${q_{{\rm SLM}}}$, and the waist of the beam at the high NA lens ${w_{{\rm lens}}}$ [see Eq. (1)]. The waist ${w_{{\rm lens}}}$ is constrained by the target waist size at the atoms ${w_{\rm a}}$, the focal length of the high NA lens, and the wavelength of the light. We calculated ${D_{{\rm max}}}$ for a number of configurations where the wavelength is 459 nm, the focal length of the high NA lens is ${23}\;{\rm mm}$, and ${q_{{\rm SLM}}} = 5$. For this configuration, we observed that AOD B is needed to avoid beam clipping and coma even for a small number of SLM partitions and moderate ${w_{\rm a}}$. Note that a lens with $NA = 0.7$ and the given focal length has a diameter of 45 mm.
Table 2.
Examples of SLM, AOD, and Beam Size Settings for Configuration 1a
Configuration 1 Addressing Examples
Qubit Array
SLM Partitions
Average Transition Rate
Burst Transition Rate
52
39
181
70
22
190
180
4
198
For each example, the following quantities are listed in columns left to right: the total qubit array size ${N_q} \times {N_q}$, number of partitions into which the SLM is divided, the ratio of the beam waist in AOD A (see Fig. 3) to the AOD crystal length (${q_{{\rm AOD,A}}}$), the average transition rate between different addressing patterns, and the burst rate between SLM resets. Each setting is consistent with a $1000 \times 1000$ pixel SLM, 2D AODs with $11.5\;{\unicode{x00B5} \rm s}$ transition time and time-bandwidth product of $TBW = 575$, SLM patch size to beam waist on the SLM ratio of ${q_{{\rm SLM}}} = 5$, and array spacing to beam waist ratio of ${q_a} = 3$.
Table 3.
Examples of SLM and Beam Size Settings for Configuration 2a
Configuration 2 Addressing Examples
Array Size
SLM Partitions
Subarray Size
Transition Rate
2
90
30
650
3
45
15
325
4
27
9
195
2
72
20
416
30
8
173
30
3.6
78
For each example, the following quantities are listed in columns left to right: the total qubit array size, number of partitions into which the SLM is divided, the dimensions of the subarray that each SLM patch addresses, the maximum simultaneous addressing number ${k_{{\rm max}}}$ for which ${P_{{\rm tot}}}$ [see Eq. (17)] is less than or equal to the number of SLM partitions, the ratio of the beam waist in AOD A (see Fig. 1) to the AOD active aperture length (${q_{{\rm AOD,A}}}$), the ratio of beam waist in AOD C to the active aperture length (${q_{{\rm AOD,C}}}$), and the average transition rate between different addressing patterns. Note that in the last two rows ${k_{{\rm max}}}$ is 2, but more than half of the three beam combinations could be included in the SLM partitions. Each of these settings is consistent with a $1000 \times 1000$ pixel SLM, 2D AODs with 11.5 µs transition time, $TBW = 575$, SLM patch size to beam waist on the SLM ratio ${q_{{\rm SLM}}} = 5$, and an array spacing to beam waist ratio of ${q_{\rm a}} = 3$.
Table 4.
SLM Patterns for Different Qubit Addressing Patterns in Configuration 2a
Configuration 2 SLM Partitions
Addressed Qubit Sub-Region
Simultaneously Addressed Sites
Unique Configurations
2
13
3
61
4
158
2
25
3
229
2
41
3
621
In configuration 2, the diffracted pattern from the SLM can be translated with respect to the array using AOD C. With this degree of freedom, the SLM only must address a subregion to address the full qubit array. The number of SLM patches needed for arbitrary addressing of this subregion depends on the dimensions of the subregion (${m_s} \times {n_s}$) and the maximum number of qubit sites to be simultaneously addressed (${k_{{\rm max}}}$). The total number of SLM patches needed to arbitrarily address any combination of sites up to ${k_{{\rm max}}}$ sites simultaneously in the subregion is then equal to ${P_{{\rm tot}}}({m_s},{n_s},{k_{{\rm max}}})$.
Add to BibSonomy
