Atomic Coherence and its Potential Applications

Tunable Photonic Bandgaps Induced by Standing-Wave Fields and Related Topics

Author(s): Jin-Hui Wu, M. Artoni, G. C. La Rocca and Jin-Yue Gao

Pp: 100-127 (28)

DOI: 10.2174/978160805085711001010100

* (Excluding Mailing and Handling)

Abstract

In this chapter, we give a brief review of our recent research works on photonic bandgaps induced by standing-wave (SW) coupling fields in the regime of electromagnetically induced transparency (EIT). EIT refers to the absorption suppression or elimination of a weak probe going through an atomic ensemble at the presence of a strong coupling, which is a result of laser induced destructive quantum interference. On the other hand, a light signal cannot freely propagate in the media with periodic refractive indices (the so-called photonic crystals) if its carrier frequencies fall inside the photonic bandgaps. Utilizing a SW coupling to attain the periodically modulated refractive index with little absorption, one can establish an induced photonic bandgap with its width and position dynamically tunable. The potential media may be either cold atomic ensembles or solid materials exhibiting defect states, such as Pr3+: Y2SiO5 and diamond containing N-V color centers. We first consider the steady optical responses of the atomic and solid media with dynamically induced bandgaps to a time- independent probe by focusing on the dispersion curves of Bloch wave vectors and the spectra of reflection and transmission. Then, we examine the propagation dynamics of a probe pulse through a cold atomic sample in two different situations where a dynamically induced bandgap exists or not. We find that the SW coupling field can be easily modulated to mold the traveling-light flow and to control the stationary-light generation with quite high flexibility, and thus may have applications in the fields of classical and quantum information processing of optical signals. In performing theoretical simulations, we also demonstrated several different but almost equivalent mathematical methods, i.e. the two-mode approximation method, the transfer-matrix method, and the Maxwell-Liouville equation method, to deal with the problems of SW-EIT. Comparison of these methods is quite helpful to understand the underlying physics of the formation of dynamically induced photonic bandgaps.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59349287 and j.to_ip >=59349287 )) and ((j.from_date <= 1740472909 and j.to_date >= 1740472909 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 574) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59349287 and j.to_ip >=59349287 )) and ((j.from_date <= 1740472909 and j.to_date >= 1740472909 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 574) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59349287 and j.to_ip >=59349287 )) and ((j.from_date <= 1740472909 and j.to_date >= 1740472909 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 574)
      600μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 831 and `b`.`banner_from_date` <= 1740472909 and `b`.`banner_to_date` >= 1740472909 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.09msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 831
      • 3: 1740472909
      • 4: 1740472909
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='f527c45acb2e54a0546445b3f99f65e8'
      300μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Keywords
    1Keywords.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        gwB8JmVRNwVKQUsGsQn5qdUESa54VAuQvUkRwQwI
        uc_cart_id
        f527c45acb2e54a0546445b3f99f65e8
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/574" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/574
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IlJZZHBjUEtvQXFvc2dpbVg1ekJnUEE9PSIsInZhbHVlIjoiSzYrK0JHWVdqKzR6bGRpSWZValRWZ0Vid3VWMlN0QVVGVVJ4QThIRHBXRT0iLCJtYWMiOiIxZGMxMzc3ZTE0ZTkzNzFhYzAwNDMzMTM4OGUzZWJmYmMxOWI3ZmMwMjM2NTJjZGM5MmFmMWY2Y2M5YTcxYWMyIiwidGFnIjoiIn0%3D; _ga_9F3B5VV3T3=GS1.1.1740472902.1.0.1740472902.60.0.0; _ga=GA1.1.78090474.1740472903wayfindertarget=eyJpdiI6IlJZZHBjUEtvQXFvc2dpbVg1ekJnUEE9PSIsInZhbHVlIjoiSzYrK0JHWVdqKzR6bGRpSWZValRWZ0Vid3VWMlN0QVVGVVJ4QThIRHBXRT0iLCJtYWMiOiIxZGMxMzc3ZTE0ZTkz" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:3 [ "wayfindertarget" => null "_ga_9F3B5VV3T3" => null "_ga" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 08:41:49 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjBGZXh1NUh0Q0JWUC9EbnkxQWFGTnc9PSIsInZhbHVlIjoiZm84ZER0ZWdMQ2R2N3V1Y0N3bVZES2RHenlvMk9aeFpFRjBDMDFBNlk4TlR2Wi9odVN1TmdOSHZLNGRobkJPTDdzZnVtZUE5WU1yazlHRU5zdUQ0eWNtYlUwdElwTU0yWHk2V0V0cG9DcEZ0YmlmRlI5ZzFEcUluSmo2WDUvNGoiLCJtYWMiOiI2MWI1NjEyNzUwYTQ4NGE0YzE0ZTBmOWEwMmJkOTZmMGY1ZDJjMmUwODliNTI0YWZkNjFlZTM4NDczYmM3ZGI4IiwidGFnIjoiIn0%3D; expires=Thu, 27 Feb 2025 20:41:49 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6IjBGZXh1NUh0Q0JWUC9EbnkxQWFGTnc9PSIsInZhbHVlIjoiZm84ZER0ZWdMQ2R2N3V1Y0N3bVZES2RHenlvMk9aeFpFRjBDMDFBNlk4TlR2Wi9odVN1TmdOSHZLNGRobkJPTDdzZnVtZ" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImVoVXFjWTVmWCtCZThrRWlIcDRoU2c9PSIsInZhbHVlIjoieU1LSFRlalRreVJqR2p4QmRyNGtCUnY4QWxSREhuUFJrbjIzaUc1bC9aUVRvcVlUV25IMWN3TUY4RHU1UWNGNGFiQWh2ZkVCWkcxM1pFSWZIVVl6bXBSc0ZLQ1Y0RVl5UDQ2UkNLMzFWS3Yrc09UdHdSTUpwSE84SnAva3hqZmciLCJtYWMiOiIwZGY2NzU4MGYxNzA5MmUzZTFlMDRlYTNjODJjZjQ0N2U0ZDNlZjBkMzUwYTQzNjAyYmM3MWYzOTA5YmY5MjliIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6ImVoVXFjWTVmWCtCZThrRWlIcDRoU2c9PSIsInZhbHVlIjoieU1LSFRlalRreVJqR2p4QmRyNGtCUnY4QWxSREhuUFJrbjIzaUc1bC9aUVRvcVlUV25IMWN3TUY" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjBGZXh1NUh0Q0JWUC9EbnkxQWFGTnc9PSIsInZhbHVlIjoiZm84ZER0ZWdMQ2R2N3V1Y0N3bVZES2RHenlvMk9aeFpFRjBDMDFBNlk4TlR2Wi9odVN1TmdOSHZLNGRobkJPTDdzZnVtZUE5WU1yazlHRU5zdUQ0eWNtYlUwdElwTU0yWHk2V0V0cG9DcEZ0YmlmRlI5ZzFEcUluSmo2WDUvNGoiLCJtYWMiOiI2MWI1NjEyNzUwYTQ4NGE0YzE0ZTBmOWEwMmJkOTZmMGY1ZDJjMmUwODliNTI0YWZkNjFlZTM4NDczYmM3ZGI4IiwidGFnIjoiIn0%3D; expires=Thu, 27-Feb-2025 20:41:49 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6IjBGZXh1NUh0Q0JWUC9EbnkxQWFGTnc9PSIsInZhbHVlIjoiZm84ZER0ZWdMQ2R2N3V1Y0N3bVZES2RHenlvMk9aeFpFRjBDMDFBNlk4TlR2Wi9odVN1TmdOSHZLNGRobkJPTDdzZnVtZ" 1 => "alphaeurekaselectnet_session=eyJpdiI6ImVoVXFjWTVmWCtCZThrRWlIcDRoU2c9PSIsInZhbHVlIjoieU1LSFRlalRreVJqR2p4QmRyNGtCUnY4QWxSREhuUFJrbjIzaUc1bC9aUVRvcVlUV25IMWN3TUY4RHU1UWNGNGFiQWh2ZkVCWkcxM1pFSWZIVVl6bXBSc0ZLQ1Y0RVl5UDQ2UkNLMzFWS3Yrc09UdHdSTUpwSE84SnAva3hqZmciLCJtYWMiOiIwZGY2NzU4MGYxNzA5MmUzZTFlMDRlYTNjODJjZjQ0N2U0ZDNlZjBkMzUwYTQzNjAyYmM3MWYzOTA5YmY5MjliIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6ImVoVXFjWTVmWCtCZThrRWlIcDRoU2c9PSIsInZhbHVlIjoieU1LSFRlalRreVJqR2p4QmRyNGtCUnY4QWxSREhuUFJrbjIzaUc1bC9aUVRvcVlUV25IMWN3TUY" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "gwB8JmVRNwVKQUsGsQn5qdUESa54VAuQvUkRwQwI" "uc_cart_id" => "f527c45acb2e54a0546445b3f99f65e8" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/574" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 08:41:49GET/chapter/574112193