Como injetar java.util.logging.Logger com CDI?

Estou tentando injetar java.util.logging.Logger mas dá o seguinte erro:

Exception during lifecycle processing
org.glassfish.deployment.common.DeploymentException: CDI deployment failure:WELD-001408: Unsatisfied 
dependencies for type Logger with qualifiers @Default
at injection point [BackedAnnotatedField] @Inject private transient controller.LoginAdminBean.logger
at controller.LoginAdminBean.logger(LoginAdminBean.java:0)
at org.glassfish.weld.WeldDeployer.event(WeldDeployer.java:234)
at org.glassfish.kernel.event.EventsImpl.send(EventsImpl.java:131)
at org.glassfish.internal.data.ApplicationInfo.load(ApplicationInfo.java:328)
at com.sun.enterprise.v3.server.ApplicationLifecycle.deploy(ApplicationLifecycle.java:496)
at com.sun.enterprise.v3.server.ApplicationLifecycle.deploy(ApplicationLifecycle.java:219)
at org.glassfish.deployment.admin.DeployCommand.execute(DeployCommand.java:491)
at com.sun.enterprise.v3.admin.CommandRunnerImpl$2$1.run(CommandRunnerImpl.java:539)
at com.sun.enterprise.v3.admin.CommandRunnerImpl$2$1.run(CommandRunnerImpl.java:535)
at java.security.AccessController.doPrivileged(Native Method)
at javax.security.auth.Subject.doAs(Subject.java:360)
at com.sun.enterprise.v3.admin.CommandRunnerImpl$2.execute(CommandRunnerImpl.java:534)
at com.sun.enterprise.v3.admin.CommandRunnerImpl$3.run(CommandRunnerImpl.java:565)
at com.sun.enterprise.v3.admin.CommandRunnerImpl$3.run(CommandRunnerImpl.java:557)
at java.security.AccessController.doPrivileged(Native Method)
at javax.security.auth.Subject.doAs(Subject.java:360)
at com.sun.enterprise.v3.admin.CommandRunnerImpl.doCommand(CommandRunnerImpl.java:556)
at com.sun.enterprise.v3.admin.CommandRunnerImpl.doCommand(CommandRunnerImpl.java:1464)
at com.sun.enterprise.v3.admin.CommandRunnerImpl.access$1300(CommandRunnerImpl.java:109)
at 
com.sun.enterprise.v3.admin.CommandRunnerImpl$ExecutionContext.execute(CommandRunnerImpl.java:1846)
at 
com.sun.enterprise.v3.admin.CommandRunnerImpl$ExecutionContext.execute(CommandRunnerImpl.java:1722)
at com.sun.enterprise.v3.admin.AdminAdapter.doCommand(AdminAdapter.java:534)
at com.sun.enterprise.v3.admin.AdminAdapter.onMissingResource(AdminAdapter.java:224)
at org.glassfish.grizzly.http.server.StaticHttpHandlerBase.service(StaticHttpHandlerBase.java:189)
at com.sun.enterprise.v3.services.impl.ContainerMapper$HttpHandlerCallable.call(ContainerMapper.java:459)
at com.sun.enterprise.v3.services.impl.ContainerMapper.service(ContainerMapper.java:167)
at org.glassfish.grizzly.http.server.HttpHandler.runService(HttpHandler.java:201)
at org.glassfish.grizzly.http.server.HttpHandler.doHandle(HttpHandler.java:175)
at org.glassfish.grizzly.http.server.HttpServerFilter.handleRead(HttpServerFilter.java:235)
at org.glassfish.grizzly.filterchain.ExecutorResolver$9.execute(ExecutorResolver.java:119)
at org.glassfish.grizzly.filterchain.DefaultFilterChain.executeFilter(DefaultFilterChain.java:284)
at org.glassfish.grizzly.filterchain.DefaultFilterChain.executeChainPart(DefaultFilterChain.java:201)
at org.glassfish.grizzly.filterchain.DefaultFilterChain.execute(DefaultFilterChain.java:133)
at org.glassfish.grizzly.filterchain.DefaultFilterChain.process(DefaultFilterChain.java:112)
at org.glassfish.grizzly.ProcessorExecutor.execute(ProcessorExecutor.java:77)
at org.glassfish.grizzly.nio.transport.TCPNIOTransport.fireIOEvent(TCPNIOTransport.java:561)
at org.glassfish.grizzly.strategies.AbstractIOStrategy.fireIOEvent(AbstractIOStrategy.java:112)
at org.glassfish.grizzly.strategies.WorkerThreadIOStrategy.run0(WorkerThreadIOStrategy.java:117)
at org.glassfish.grizzly.strategies.WorkerThreadIOStrategy.access$100(WorkerThreadIOStrategy.java:56)
at  org.glassfish.grizzly.strategies.WorkerThreadIOStrategy$WorkerThreadRunnable.run(WorkerThreadIOStrategy.java:137)
at org.glassfish.grizzly.threadpool.AbstractThreadPool$Worker.doWork(AbstractThreadPool.java:565)
at org.glassfish.grizzly.threadpool.AbstractThreadPool$Worker.run(AbstractThreadPool.java:545)
at java.lang.Thread.run(Thread.java:745)
Caused by: org.jboss.weld.exceptions.DeploymentException: WELD-001408: Unsatisfied dependencies for type 
Logger with qualifiers @Default
 at injection point [BackedAnnotatedField] @Inject private transient controller.LoginAdminBean.logger
  at controller.LoginAdminBean.logger(LoginAdminBean.java:0)

pagina jsf

<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"
  xmlns:h="http://xmlns.jcp.org/jsf/html">
<h:head>
    <title>Login</title>
</h:head>
<h:body>
    <h:messages/>
    <h:form>            
        <h:panelGrid columns="2">
            <h:outputText value="CPF" />
            <h:inputText id="cpf" value="#{loginAdminBean.adm.cpf}" label="CPF" />
            <h:outputText value="Senha" />
            <h:inputSecret id="senha" value="#{loginAdminBean.adm.senha}" label="Senha" />
        </h:panelGrid>
        <h:commandButton value="Logar" action="#{loginAdminBean.logar()}" />
    </h:form>
</h:body>

LoginBean

@SessionScoped
@Model
public class LoginAdminBean implements Serializable{

@Inject @LoginBeanV2
private LoginService loginService;  
//tentando injetar java.util.logging.Logger
@Inject
private transient Logger logger;

private SysUser adm = new SysUser();        

public String logar(){
    
    adm = loginService.logar(adm);
    
    if(adm.getId() != null){
        
        logger.info("Usuário CPF: " +adm.getCpf() +" logou. OK");
        return "adm/index";            
    }            
    
    FacesContext.getCurrentInstance().addMessage(null, new FacesMessage("Login Inválido"));        
    return null;
 }   
}

logger

public class LogginProducer {
    
 @Produces
 private Logger createLogger(InjectionPoint injectionPoint){
    
    return Logger.getLogger(injectionPoint.getMember().getDeclaringClass().getName());
 }    
}    

pom.xml

<dependencies>                        
    <dependency>
        <groupId>javax</groupId>
        <artifactId>javaee-api</artifactId>
        <version>7.0</version>
        <scope>provided</scope>
    </dependency>                
    <dependency>
        <groupId>org.hibernate</groupId>
        <artifactId>hibernate-core</artifactId>
        <version>4.3.5.Final</version>
    </dependency>
    <dependency>
        <groupId>org.hibernate</groupId>
        <artifactId>hibernate-entitymanager</artifactId>
        <version>4.3.5.Final</version>
    </dependency>
    <dependency>
        <groupId>postgresql</groupId>
        <artifactId>postgresql</artifactId>
        <version>9.1-901.jdbc4</version>
    </dependency>
    <dependency>
        <groupId>org.hibernate</groupId>
        <artifactId>hibernate-validator</artifactId>
        <version>5.3.5.Final</version>
    </dependency>        
</dependencies>

servidor glassFish 4.